[{"status":"public","type":"journal_article","article_type":"original","_id":"3649","extern":"1","date_updated":"2022-02-23T14:48:49Z","month":"01","intvolume":" 38","scopus_import":"1","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/004058099090002D?via%3Dihub"}],"oa_version":"None","abstract":[{"lang":"eng","text":"Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations."}],"issue":"1","volume":38,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0040-5809"]},"publication_status":"published","title":"Dynamics of polygenic characters under selection","publist_id":"2734","author":[{"first_name":"Michael","last_name":"Turelli","full_name":"Turelli, Michael"},{"first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","last_name":"Barton","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240"}],"article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Turelli, Michael, and Nicholas H. Barton. “Dynamics of Polygenic Characters under Selection.” Theoretical Population Biology, vol. 38, no. 1, Academic Press, 1990, pp. 1–57, doi:10.1016/0040-5809(90)90002-D.","short":"M. Turelli, N.H. Barton, Theoretical Population Biology 38 (1990) 1–57.","ieee":"M. Turelli and N. H. Barton, “Dynamics of polygenic characters under selection,” Theoretical Population Biology, vol. 38, no. 1. Academic Press, pp. 1–57, 1990.","ama":"Turelli M, Barton NH. Dynamics of polygenic characters under selection. Theoretical Population Biology. 1990;38(1):1-57. doi:10.1016/0040-5809(90)90002-D","apa":"Turelli, M., & Barton, N. H. (1990). Dynamics of polygenic characters under selection. Theoretical Population Biology. Academic Press. https://doi.org/10.1016/0040-5809(90)90002-D","chicago":"Turelli, Michael, and Nicholas H Barton. “Dynamics of Polygenic Characters under Selection.” Theoretical Population Biology. Academic Press, 1990. https://doi.org/10.1016/0040-5809(90)90002-D.","ista":"Turelli M, Barton NH. 1990. Dynamics of polygenic characters under selection. Theoretical Population Biology. 38(1), 1–57."},"quality_controlled":"1","publisher":"Academic Press","acknowledgement":"We thank R. Burger, J. A. Coyne, W. G. Hill, A. A. Hoffmann, J. H. Gillespie, M. Slatkin, T. Nagylaki and Z.-B. Zeng for helpful discussions and comments on earlier drafts. Our research is supported by grants from the National Science Foundation (BSR-8866548), the Science and Engineering Research Council, and the Institute of Theoretical Dynamics at UCD. ","doi":"10.1016/0040-5809(90)90002-D","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:04:26Z","page":"1 - 57","day":"01","publication":"Theoretical Population Biology","year":"1990"},{"citation":{"short":"N.H. Barton, Genetics 124 (1990) 773–782.","ieee":"N. H. Barton, “Pleiotropic models of quantitative variation,” Genetics, vol. 124, no. 3. Genetics Society of America, pp. 773–782, 1990.","apa":"Barton, N. H. (1990). Pleiotropic models of quantitative variation. Genetics. Genetics Society of America. https://doi.org/10.1093/genetics/124.3.773 ","ama":"Barton NH. Pleiotropic models of quantitative variation. Genetics. 1990;124(3):773-782. doi:10.1093/genetics/124.3.773 ","mla":"Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” Genetics, vol. 124, no. 3, Genetics Society of America, 1990, pp. 773–82, doi:10.1093/genetics/124.3.773 .","ista":"Barton NH. 1990. Pleiotropic models of quantitative variation. Genetics. 124(3), 773–782.","chicago":"Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” Genetics. Genetics Society of America, 1990. https://doi.org/10.1093/genetics/124.3.773 ."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H"}],"publist_id":"2732","external_id":{"pmid":["2311921"]},"article_processing_charge":"No","title":"Pleiotropic models of quantitative variation","year":"1990","day":"01","publication":"Genetics","page":"773 - 782","doi":"10.1093/genetics/124.3.773 ","date_published":"1990-03-01T00:00:00Z","date_created":"2018-12-11T12:04:26Z","acknowledgement":"Thanks to JERRY COYNE, BILL HILL, LINDA PARTRIDGE, MICHAEL TURELLI, and two anonymous reviewers for their critical comments. This work was supported by grants from the National Science Foundation (BSR-8866548) the Science and Engineering Research Council (GR/E/08507), and by the Institute of Theoretical Dynamics, University of California, Davis.","publisher":"Genetics Society of America","quality_controlled":"1","oa":1,"date_updated":"2022-02-23T10:41:43Z","extern":"1","_id":"3651","article_type":"original","type":"journal_article","status":"public","publication_identifier":{"issn":["0016-6731"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":124,"abstract":[{"lang":"eng","text":"It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s & 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed."}],"pmid":1,"oa_version":"Published Version","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://academic.oup.com/genetics/article/124/3/773/5999956?login=true"}],"month":"03","intvolume":" 124"},{"doi":"10.1007/3-540-52921-7_91","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:06:45Z","page":"419 - 428","day":"01","publication":"Proceedings of the International Symposium on Algorithms","year":"1990","publisher":"Springer","quality_controlled":"1","acknowledgement":"Research of the first author was supported by the National Science Foundation under grant CCR-8714565. Work of the second author was supported by Office of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD — the Israeli National Council for Research and Development, and the Fund for Basic Research in Electronics, Computers and Communication administered by the Israeli Academy of Sciences.","title":"A hyperplane Incidence problem with applications to counting distances","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Sharir","full_name":"Sharir, Micha","first_name":"Micha"}],"publist_id":"2056","article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” Proceedings of the International Symposium on Algorithms, vol. 450, Springer, 1990, pp. 419–28, doi:10.1007/3-540-52921-7_91.","ama":"Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications to counting distances. In: Proceedings of the International Symposium on Algorithms. Vol 450. Springer; 1990:419-428. doi:10.1007/3-540-52921-7_91","apa":"Edelsbrunner, H., & Sharir, M. (1990). A hyperplane Incidence problem with applications to counting distances. In Proceedings of the International Symposium on Algorithms (Vol. 450, pp. 419–428). Tokyo, Japan: Springer. https://doi.org/10.1007/3-540-52921-7_91","ieee":"H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications to counting distances,” in Proceedings of the International Symposium on Algorithms, Tokyo, Japan, 1990, vol. 450, pp. 419–428.","short":"H. Edelsbrunner, M. Sharir, in:, Proceedings of the International Symposium on Algorithms, Springer, 1990, pp. 419–428.","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” In Proceedings of the International Symposium on Algorithms, 450:419–28. Springer, 1990. https://doi.org/10.1007/3-540-52921-7_91.","ista":"Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications to counting distances. Proceedings of the International Symposium on Algorithms. SIGAL: Special Interest Group on Algorithms, International Symposium on Algorithms , LNCS, vol. 450, 419–428."},"volume":450,"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-540-52921-7"]},"publication_status":"published","month":"01","intvolume":" 450","scopus_import":"1","alternative_title":["LNCS"],"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-52921-7_91"}],"oa_version":"None","abstract":[{"lang":"eng","text":"This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem."}],"extern":"1","date_updated":"2022-02-22T14:31:26Z","status":"public","type":"conference","conference":{"name":"SIGAL: Special Interest Group on Algorithms, International Symposium on Algorithms ","start_date":"1990-08-16","end_date":"1990-08-18","location":"Tokyo, Japan"},"_id":"4067"},{"citation":{"mla":"Edelsbrunner, Herbert, et al. “The Complexity of Many Cells in Arrangements of Planes and Related Problems.” Discrete & Computational Geometry, vol. 5, no. 1, Springer, 1990, pp. 197–216, doi:10.1007/BF02187785.","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity of many cells in arrangements of planes and related problems,” Discrete & Computational Geometry, vol. 5, no. 1. Springer, pp. 197–216, 1990.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry 5 (1990) 197–216.","apa":"Edelsbrunner, H., Guibas, L., & Sharir, M. (1990). The complexity of many cells in arrangements of planes and related problems. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187785","ama":"Edelsbrunner H, Guibas L, Sharir M. The complexity of many cells in arrangements of planes and related problems. Discrete & Computational Geometry. 1990;5(1):197-216. doi:10.1007/BF02187785","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity of Many Cells in Arrangements of Planes and Related Problems.” Discrete & Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187785.","ista":"Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity of many cells in arrangements of planes and related problems. Discrete & Computational Geometry. 5(1), 197–216."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"}],"publist_id":"2054","article_processing_charge":"No","title":"The complexity of many cells in arrangements of planes and related problems","acknowledgement":"Supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by NSF Grant CCR-8714565. Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. I-6-44862 and by NSF Grant CCR-87t4565. Work by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD--the Israeli National Council for Research and Development. An abstract of this\r\npaper has appeared in the Proceedings of the 13th International Mathematical Programming Symposium, Tokyo, 1988, p. 147","publisher":"Springer","quality_controlled":"1","year":"1990","day":"01","publication":"Discrete & Computational Geometry","page":"197 - 216","date_published":"1990-03-01T00:00:00Z","doi":"10.1007/BF02187785","date_created":"2018-12-11T12:06:44Z","_id":"4066","type":"journal_article","article_type":"original","status":"public","date_updated":"2022-02-22T11:02:41Z","extern":"1","abstract":[{"text":"We consider several problems involving points and planes in three dimensions. Our main results are: (i) The maximum number of faces boundingm distinct cells in an arrangement ofn planes isO(m 2/3 n logn +n 2); we can calculatem such cells specified by a point in each, in worst-case timeO(m 2/3 n log3 n+n 2 logn). (ii) The maximum number of incidences betweenn planes andm vertices of their arrangement isO(m 2/3 n logn+n 2), but this number is onlyO(m 3/5– n 4/5+2 +m+n logm), for any>0, for any collection of points no three of which are collinear. (iii) For an arbitrary collection ofm points, we can calculate the number of incidences between them andn planes by a randomized algorithm whose expected time complexity isO((m 3/4– n 3/4+3 +m) log2 n+n logn logm) for any>0. (iv) Givenm points andn planes, we can find the plane lying immediately below each point in randomized expected timeO([m 3/4– n 3/4+3 +m] log2 n+n logn logm) for any>0. (v) The maximum number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an arrangement ofn hyperplanes ind dimensions,d>3, isO(m 2/3 n d/3 logn+n d–1). This is also an upper bound for the number of incidences betweenn hyperplanes ind dimensions andm vertices of their arrangement. The combinatorial bounds in (i) and (v) and the general bound in (ii) are almost tight.","lang":"eng"}],"oa_version":"None","scopus_import":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187785"}],"month":"03","intvolume":" 5","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":5},{"issue":"1","volume":5,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"intvolume":" 5","month":"01","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187784"}],"scopus_import":"1","oa_version":"None","abstract":[{"lang":"eng","text":"We show that the total number of edges ofm faces of an arrangement ofn lines in the plane isO(m 2/3– n 2/3+2 +n) for any>0. The proof takes an algorithmic approach, that is, we describe an algorithm for the calculation of thesem faces and derive the upper bound from the analysis of the algorithm. The algorithm uses randomization and its expected time complexity isO(m 2/3– n 2/3+2 logn+n logn logm). If instead of lines we have an arrangement ofn line segments, then the maximum number of edges ofm faces isO(m 2/3– n 2/3+2 +n (n) logm) for any>0, where(n) is the functional inverse of Ackermann's function. We give a (randomized) algorithm that produces these faces and takes expected timeO(m 2/3– n 2/3+2 log+n(n) log2 n logm)."}],"extern":"1","date_updated":"2022-02-22T09:27:30Z","status":"public","article_type":"original","type":"journal_article","_id":"4072","date_created":"2018-12-11T12:06:46Z","date_published":"1990-01-01T00:00:00Z","doi":"10.1007/BF02187784","page":"161 - 196","publication":"Discrete & Computational Geometry","day":"01","year":"1990","quality_controlled":"1","publisher":"Springer","acknowledgement":"The first author is pleased to acknowledge partial support by the Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and the National Science Foundation under Grant CCR-8714565. Work on this paper by the third author has been supported by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation Grant DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD-the Israeli National Council for Research and Development. A preliminary version of this paper has appeared in theProceedings of the 4th ACM Symposium on Computational Geometry, 1988, pp. 44–55.","title":"The complexity and construction of many faces in arrangements of lines and of segments","article_processing_charge":"No","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Leonidas","full_name":"Guibas, Leonidas","last_name":"Guibas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"publist_id":"2053","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"ista":"Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity and construction of many faces in arrangements of lines and of segments. Discrete & Computational Geometry. 5(1), 161–196.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity and Construction of Many Faces in Arrangements of Lines and of Segments.” Discrete & Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187784.","ama":"Edelsbrunner H, Guibas L, Sharir M. The complexity and construction of many faces in arrangements of lines and of segments. Discrete & Computational Geometry. 1990;5(1):161-196. doi:10.1007/BF02187784","apa":"Edelsbrunner, H., Guibas, L., & Sharir, M. (1990). The complexity and construction of many faces in arrangements of lines and of segments. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187784","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity and construction of many faces in arrangements of lines and of segments,” Discrete & Computational Geometry, vol. 5, no. 1. Springer, pp. 161–196, 1990.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry 5 (1990) 161–196.","mla":"Edelsbrunner, Herbert, et al. “The Complexity and Construction of Many Faces in Arrangements of Lines and of Segments.” Discrete & Computational Geometry, vol. 5, no. 1, Springer, 1990, pp. 161–96, doi:10.1007/BF02187784."}},{"title":"Counting and cutting cycles of lines and rods in space","article_processing_charge":"No","publist_id":"2047","author":[{"last_name":"Chazelle","full_name":"Chazelle, Bernard","first_name":"Bernard"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"first_name":"Richard","last_name":"Pollack","full_name":"Pollack, Richard"},{"first_name":"Raimund","full_name":"Seidel, Raimund","last_name":"Seidel"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"},{"last_name":"Snoeyink","full_name":"Snoeyink, Jack","first_name":"Jack"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","date_updated":"2022-02-17T11:07:07Z","citation":{"ista":"Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink J. 1990. Counting and cutting cycles of lines and rods in space. 31st Annual Symposium on Foundations of Computer Science. FOCS: Foundations of Computer Science, 242–251.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Richard Pollack, Raimund Seidel, Micha Sharir, and Jack Snoeyink. “Counting and Cutting Cycles of Lines and Rods in Space.” In 31st Annual Symposium on Foundations of Computer Science, 242–51. IEEE, 1990. https://doi.org/10.1109/FSCS.1990.89543.","ama":"Chazelle B, Edelsbrunner H, Guibas L, et al. Counting and cutting cycles of lines and rods in space. In: 31st Annual Symposium on Foundations of Computer Science. IEEE; 1990:242-251. doi:10.1109/FSCS.1990.89543","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., Pollack, R., Seidel, R., Sharir, M., & Snoeyink, J. (1990). Counting and cutting cycles of lines and rods in space. In 31st Annual Symposium on Foundations of Computer Science (pp. 242–251). St. Louis, MO, United States of America: IEEE. https://doi.org/10.1109/FSCS.1990.89543","ieee":"B. Chazelle et al., “Counting and cutting cycles of lines and rods in space,” in 31st Annual Symposium on Foundations of Computer Science, St. Louis, MO, United States of America, 1990, pp. 242–251.","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink, in:, 31st Annual Symposium on Foundations of Computer Science, IEEE, 1990, pp. 242–251.","mla":"Chazelle, Bernard, et al. “Counting and Cutting Cycles of Lines and Rods in Space.” 31st Annual Symposium on Foundations of Computer Science, IEEE, 1990, pp. 242–51, doi:10.1109/FSCS.1990.89543."},"status":"public","conference":{"location":"St. Louis, MO, United States of America","end_date":"1990-10-24","start_date":"1990-10-22","name":"FOCS: Foundations of Computer Science"},"type":"conference","_id":"4073","date_created":"2018-12-11T12:06:47Z","date_published":"1990-01-01T00:00:00Z","doi":"10.1109/FSCS.1990.89543","page":"242 - 251","publication":"31st Annual Symposium on Foundations of Computer Science","language":[{"iso":"eng"}],"day":"01","publication_status":"published","year":"1990","publication_identifier":{"isbn":["0-8186-2082-X"]},"month":"01","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/89543"}],"quality_controlled":"1","publisher":"IEEE","scopus_import":"1","oa_version":"None","abstract":[{"lang":"eng","text":"A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered."}]},{"abstract":[{"text":"Let S be a set of n closed intervals on the x-axis. A ranking assigns to each interval, s, a distinct rank, p(s)∊ [1, 2,…,n]. We say that s can see t if p(s)
International Journal of Computer Mathematics. Taylor & Francis. https://doi.org/10.1080/00207169008803871","ama":"Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. Ranking intervals under visibility constraints. International Journal of Computer Mathematics. 1990;34(3-4):129-144. doi:10.1080/00207169008803871","short":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International Journal of Computer Mathematics 34 (1990) 129–144.","ieee":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, and J. Feldman, “Ranking intervals under visibility constraints,” International Journal of Computer Mathematics, vol. 34, no. 3–4. Taylor & Francis, pp. 129–144, 1990.","mla":"Edelsbrunner, Herbert, et al. “Ranking Intervals under Visibility Constraints.” International Journal of Computer Mathematics, vol. 34, no. 3–4, Taylor & Francis, 1990, pp. 129–44, doi:10.1080/00207169008803871.","ista":"Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. 1990. Ranking intervals under visibility constraints. International Journal of Computer Mathematics. 34(3–4), 129–144.","chicago":"Edelsbrunner, Herbert, Mark Overmars, Emo Welzl, Irith Hartman, and Jack Feldman. “Ranking Intervals under Visibility Constraints.” International Journal of Computer Mathematics. Taylor & Francis, 1990. https://doi.org/10.1080/00207169008803871."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_processing_charge":"No","publist_id":"2051","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Mark","full_name":"Overmars, Mark","last_name":"Overmars"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"},{"first_name":"Irith","full_name":"Hartman, Irith","last_name":"Hartman"},{"last_name":"Feldman","full_name":"Feldman, Jack","first_name":"Jack"}],"title":"Ranking intervals under visibility constraints"},{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","citation":{"ista":"Edelsbrunner H, Tan T, Waupotitsch R. 1990. An O(n^2log n) time algorithm for the MinMax angle triangulation. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 44–52.","chicago":"Edelsbrunner, Herbert, Tiow Tan, and Roman Waupotitsch. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” In Proceedings of the 6th Annual Symposium on Computational Geometry, 44–52. ACM, 1990. https://doi.org/10.1145/98524.98535.","short":"H. Edelsbrunner, T. Tan, R. Waupotitsch, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 44–52.","ieee":"H. Edelsbrunner, T. Tan, and R. Waupotitsch, “An O(n^2log n) time algorithm for the MinMax angle triangulation,” in Proceedings of the 6th annual symposium on Computational geometry, Berkley, CA, United States, 1990, pp. 44–52.","ama":"Edelsbrunner H, Tan T, Waupotitsch R. An O(n^2log n) time algorithm for the MinMax angle triangulation. In: Proceedings of the 6th Annual Symposium on Computational Geometry. ACM; 1990:44-52. doi:10.1145/98524.98535","apa":"Edelsbrunner, H., Tan, T., & Waupotitsch, R. (1990). An O(n^2log n) time algorithm for the MinMax angle triangulation. In Proceedings of the 6th annual symposium on Computational geometry (pp. 44–52). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98535","mla":"Edelsbrunner, Herbert, et al. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 44–52, doi:10.1145/98524.98535."},"date_updated":"2022-02-22T08:56:42Z","title":"An O(n^2log n) time algorithm for the MinMax angle triangulation","article_processing_charge":"No","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Tan","full_name":"Tan, Tiow","first_name":"Tiow"},{"full_name":"Waupotitsch, Roman","last_name":"Waupotitsch","first_name":"Roman"}],"publist_id":"2052","_id":"4071","status":"public","conference":{"start_date":"1990-06-07","location":"Berkley, CA, United States","end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry"},"type":"conference","language":[{"iso":"eng"}],"publication":"Proceedings of the 6th annual symposium on Computational geometry","day":"01","year":"1990","publication_status":"published","publication_identifier":{"isbn":["978-0-89791-362-1"]},"date_created":"2018-12-11T12:06:46Z","doi":"10.1145/98524.98535","date_published":"1990-01-01T00:00:00Z","page":"44 - 52","oa_version":"None","abstract":[{"text":"We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement.","lang":"eng"}],"month":"01","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98535"}],"publisher":"ACM","quality_controlled":"1"},{"abstract":[{"text":"LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations\r\n(i1i2in−1in)(inin−1i2i1) \r\nis called ageometric permutation of S if there is a line that intersects all sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations. This upper bound is tight.","lang":"eng"}],"oa_version":"None","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187778"}],"month":"01","intvolume":" 5","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":5,"issue":"1","_id":"4068","type":"journal_article","article_type":"original","status":"public","date_updated":"2022-02-22T14:50:34Z","extern":"1","acknowledgement":"Research of the first author was supported by Amoco Foundation for Faculty Development in Computer Science Grant No. 1-6-44862. Work on this paper by the second author was supported by Office of Naval Research Grant No. N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation.","publisher":"Springer","quality_controlled":"1","year":"1990","day":"01","publication":"Discrete & Computational Geometry","page":"35 - 42","date_published":"1990-01-01T00:00:00Z","doi":"10.1007/BF02187778","date_created":"2018-12-11T12:06:45Z","citation":{"mla":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” Discrete & Computational Geometry, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi:10.1007/BF02187778.","short":"H. Edelsbrunner, M. Sharir, Discrete & Computational Geometry 5 (1990) 35–42.","ieee":"H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2,” Discrete & Computational Geometry, vol. 5, no. 1. Springer, pp. 35–42, 1990.","apa":"Edelsbrunner, H., & Sharir, M. (1990). The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187778","ama":"Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. 1990;5(1):35-42. doi:10.1007/BF02187778","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” Discrete & Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187778.","ista":"Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. 5(1), 35–42."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"}],"publist_id":"2057","article_processing_charge":"No","title":"The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2"},{"_id":"4069","status":"public","article_type":"original","type":"journal_article","extern":"1","date_updated":"2022-02-21T11:08:30Z","oa_version":"None","abstract":[{"text":"Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.","lang":"eng"}],"intvolume":" 10","month":"09","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02122779"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"volume":10,"issue":"3","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” Combinatorica. Springer, 1990. https://doi.org/10.1007/BF02122779.","ista":"Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260.","mla":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” Combinatorica, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:10.1007/BF02122779.","short":"H. Edelsbrunner, Combinatorica 10 (1990) 251–260.","ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” Combinatorica, vol. 10, no. 3. Springer, pp. 251–260, 1990.","apa":"Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. Combinatorica. Springer. https://doi.org/10.1007/BF02122779","ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 1990;10(3):251-260. doi:10.1007/BF02122779"},"title":"An acyclicity theorem for cell complexes in d dimension","article_processing_charge":"No","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"2050","acknowledgement":"Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565.","quality_controlled":"1","publisher":"Springer","publication":"Combinatorica","day":"01","year":"1990","date_created":"2018-12-11T12:06:45Z","date_published":"1990-09-01T00:00:00Z","doi":"10.1007/BF02122779","page":"251 - 260"},{"date_updated":"2022-02-23T16:10:03Z","extern":"1","type":"journal_article","article_type":"original","status":"public","_id":"3467","volume":420,"publication_status":"published","publication_identifier":{"issn":["0022-3751"],"eissn":["1469-7793"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1190055/","open_access":"1"}],"scopus_import":"1","intvolume":" 420","month":"01","abstract":[{"lang":"eng","text":"The effects of mast cell degranulating peptide (MCDP), a toxin from the honey bee, and of dendrotoxin (DTX), a toxin from the green mamba snake, were studied in voltage-clamped experiments with myelinated nerve fibres of Xenopus. MCDP and DTX blocked part of the K+ current. About 20% of the K+ current, however, was resistant to the toxins even in high concentrations. In Ringer solution half-maximal block was reached with concentrations of 33 nM MCDP and 11 nM DTX. In high-K+ solution the potency of both toxins was lower. β-Bungarotoxin (β-BuTX), another snake toxin, also blocked part of the K+ current, but was less potent than MCDP and DTX. Tail currents in high-K+ solution were analysed and three K+ current components were separated according to Dubois (1981b). Both MCDP and DTX selectively blocked a fast deactivating, slowly inactivating K+ current component which steeply activates between E = -60 mV and E = -40 mV (component f1). In concentrations around 100 nM, MCDP and DTX blocked neither the slow K+ current (component s) nor the fast deactivating, rapidly inactivating K+ current which activates between E = -40 mV and E = 20 mV (component f2). Similar results could be derived from K+ outward currents in Ringer solution. In high-K+, IC50 of MCDP for component f1 was 99 nM, whereas it was 7.6 μM for f2. Corresponding values for DTX are 68 nM and 1.8 μM. Binding studies with nerve fibre membranes of Xenopus reveal high-affinity binding sites for 125I-labelled DTX )K(D) = 22 pM in Ringer solution and 81 pM in high-K+ solution). 125I-labelled DTX can be displaced from its sites completely by unlabelled DTX, toxin I (black mamba toxin), MCDP, and partially by β-BuTX. Immunocytochemical staining demonstrates that binding sites for DTX are present in nodal and paranodal regions of the axonal membrane. The axonal membrane of motor and sensory nerve fibres is equipped with three types of well-characterized K+ channels and constitutes so far the best preparation to study MCDP- and DTX-sensitive K+ channels with electrophysiological and biochemical methods."}],"oa_version":"None","pmid":1,"article_processing_charge":"No","external_id":{"pmid":["2324990"]},"publist_id":"2920","author":[{"first_name":"Michael","last_name":"Bräu","full_name":"Bräu, Michael"},{"first_name":"Florian","last_name":"Dreyer","full_name":"Dreyer, Florian"},{"last_name":"Jonas","full_name":"Jonas, Peter M","orcid":"0000-0001-5001-4804","first_name":"Peter M","id":"353C1B58-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Repp","full_name":"Repp, Holger","first_name":"Holger"},{"last_name":"Vogel","full_name":"Vogel, Werner","first_name":"Werner"}],"title":"A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments","citation":{"mla":"Bräu, Michael, et al. “A K+ Channel in Xenopus Nerve Fibres Selectively Blocked by Bee and Snake Toxins: Binding and Voltage-Clamp Experiments.” Journal of Physiology, vol. 420, Wiley-Blackwell, 1990, pp. 365–85, doi:10.1113/jphysiol.1990.sp017918.","ieee":"M. Bräu, F. Dreyer, P. M. Jonas, H. Repp, and W. Vogel, “A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments,” Journal of Physiology, vol. 420. Wiley-Blackwell, pp. 365–385, 1990.","short":"M. Bräu, F. Dreyer, P.M. Jonas, H. Repp, W. Vogel, Journal of Physiology 420 (1990) 365–385.","ama":"Bräu M, Dreyer F, Jonas PM, Repp H, Vogel W. A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments. Journal of Physiology. 1990;420:365-385. doi:10.1113/jphysiol.1990.sp017918","apa":"Bräu, M., Dreyer, F., Jonas, P. M., Repp, H., & Vogel, W. (1990). A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments. Journal of Physiology. Wiley-Blackwell. https://doi.org/10.1113/jphysiol.1990.sp017918","chicago":"Bräu, Michael, Florian Dreyer, Peter M Jonas, Holger Repp, and Werner Vogel. “A K+ Channel in Xenopus Nerve Fibres Selectively Blocked by Bee and Snake Toxins: Binding and Voltage-Clamp Experiments.” Journal of Physiology. Wiley-Blackwell, 1990. https://doi.org/10.1113/jphysiol.1990.sp017918.","ista":"Bräu M, Dreyer F, Jonas PM, Repp H, Vogel W. 1990. A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments. Journal of Physiology. 420, 365–385."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"365 - 385","date_created":"2018-12-11T12:03:29Z","doi":"10.1113/jphysiol.1990.sp017918","date_published":"1990-01-01T00:00:00Z","year":"1990","publication":"Journal of Physiology","day":"01","oa":1,"publisher":"Wiley-Blackwell","quality_controlled":"1","acknowledgement":"We thank Professor E. Habermann for critical reading of the manuscript and E. Schmidt and J. Schafer for technical assistance. Financial support by the Deutsche Forschungsgemeinschaft (Vo 188/13-1 and SFB 249) is gratefully acknowledged.\r\n"},{"quality_controlled":"1","publisher":"Springer","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-1-4613-8997-2_25"}],"month":"01","abstract":[{"lang":"eng","text":"We investigate the complexity of determining the shape and presentation (i.e. position with orientation) of convex polytopes in multi-dimensional Euclidean space using a variety of probe models."}],"oa_version":"None","acknowledgement":"NSF Grant MCS-83-03926 and DCR-85-05517\r\nAmoco Foundation Faculty Development in Computer Science\r\nNSF Grant DCR-84-01633 and DCR-84-01898","page":"328 - 341","date_published":"1990-01-01T00:00:00Z","doi":"10.1007/978-1-4613-8997-2_25","date_created":"2018-12-11T12:03:59Z","publication_identifier":{"isbn":["978-1-4613-8997-2"]},"year":"1990","publication_status":"published","day":"01","publication":"Autonomous Robot Vehicles","language":[{"iso":"eng"}],"type":"book_chapter","status":"public","_id":"3565","author":[{"last_name":"Dobkin","full_name":"Dobkin, David","first_name":"David"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Yap, Chee","last_name":"Yap","first_name":"Chee"}],"publist_id":"2820","article_processing_charge":"No","editor":[{"last_name":"Cox","full_name":"Cox, Ingemar","first_name":"Ingemar"},{"first_name":"Gordon","full_name":"Wilfong, Gordon","last_name":"Wilfong"}],"title":"Probing convex polytopes","date_updated":"2022-02-23T15:41:07Z","citation":{"chicago":"Dobkin, David, Herbert Edelsbrunner, and Chee Yap. “Probing Convex Polytopes.” In Autonomous Robot Vehicles, edited by Ingemar Cox and Gordon Wilfong, 328–41. Springer, 1990. https://doi.org/10.1007/978-1-4613-8997-2_25.","ista":"Dobkin D, Edelsbrunner H, Yap C. 1990.Probing convex polytopes. In: Autonomous Robot Vehicles. , 328–341.","mla":"Dobkin, David, et al. “Probing Convex Polytopes.” Autonomous Robot Vehicles, edited by Ingemar Cox and Gordon Wilfong, Springer, 1990, pp. 328–41, doi:10.1007/978-1-4613-8997-2_25.","ama":"Dobkin D, Edelsbrunner H, Yap C. Probing convex polytopes. In: Cox I, Wilfong G, eds. Autonomous Robot Vehicles. Springer; 1990:328-341. doi:10.1007/978-1-4613-8997-2_25","apa":"Dobkin, D., Edelsbrunner, H., & Yap, C. (1990). Probing convex polytopes. In I. Cox & G. Wilfong (Eds.), Autonomous Robot Vehicles (pp. 328–341). Springer. https://doi.org/10.1007/978-1-4613-8997-2_25","ieee":"D. Dobkin, H. Edelsbrunner, and C. Yap, “Probing convex polytopes,” in Autonomous Robot Vehicles, I. Cox and G. Wilfong, Eds. Springer, 1990, pp. 328–341.","short":"D. Dobkin, H. Edelsbrunner, C. Yap, in:, I. Cox, G. Wilfong (Eds.), Autonomous Robot Vehicles, Springer, 1990, pp. 328–341."},"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17"},{"quality_controlled":"1","publisher":"American Statistical Association","doi":"10.1080/01621459.1990.10475313","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:06:43Z","page":"115 - 119","day":"01","publication":"Journal of the American Statistical Association","year":"1990","title":"Computing least median of squares regression lines and guided topological sweep","publist_id":"2059","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Diane","last_name":"Souvaine","full_name":"Souvaine, Diane"}],"article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"chicago":"Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” Journal of the American Statistical Association. American Statistical Association, 1990. https://doi.org/10.1080/01621459.1990.10475313.","ista":"Edelsbrunner H, Souvaine D. 1990. Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. 85(409), 115–119.","mla":"Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” Journal of the American Statistical Association, vol. 85, no. 409, American Statistical Association, 1990, pp. 115–19, doi:10.1080/01621459.1990.10475313.","short":"H. Edelsbrunner, D. Souvaine, Journal of the American Statistical Association 85 (1990) 115–119.","ieee":"H. Edelsbrunner and D. Souvaine, “Computing least median of squares regression lines and guided topological sweep,” Journal of the American Statistical Association, vol. 85, no. 409. American Statistical Association, pp. 115–119, 1990.","apa":"Edelsbrunner, H., & Souvaine, D. (1990). Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. American Statistical Association. https://doi.org/10.1080/01621459.1990.10475313","ama":"Edelsbrunner H, Souvaine D. Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. 1990;85(409):115-119. doi:10.1080/01621459.1990.10475313"},"month":"01","intvolume":" 85","scopus_import":"1","main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10475313"}],"oa_version":"None","abstract":[{"text":"Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements.","lang":"eng"}],"volume":85,"issue":"409","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0003-1291"],"eissn":["1537-274X"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","_id":"4064","extern":"1","date_updated":"2022-02-22T15:10:54Z"},{"year":"1990","publication":"ACM Transactions on Graphics","day":"01","page":"66 - 104","date_created":"2018-12-11T12:06:43Z","date_published":"1990-01-01T00:00:00Z","doi":"10.1145/77635.77639","acknowledgement":"Research of both authors was supported by Amoco Foundation Faculty Development grant CS 1-6-44862. It was partially carried out while both authors were with the Institutes for Information Processing at the Technical University of Graz, Austria. The first author also acknowledges support by the National Science Foundation under grant CCR-8714565. ","publisher":"ACM","quality_controlled":"1","citation":{"ista":"Edelsbrunner H, Mücke E. 1990. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 9(1), 66–104.","chicago":"Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” ACM Transactions on Graphics. ACM, 1990. https://doi.org/10.1145/77635.77639.","short":"H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 9 (1990) 66–104.","ieee":"H. Edelsbrunner and E. Mücke, “Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms,” ACM Transactions on Graphics, vol. 9, no. 1. ACM, pp. 66–104, 1990.","apa":"Edelsbrunner, H., & Mücke, E. (1990). Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. ACM. https://doi.org/10.1145/77635.77639","ama":"Edelsbrunner H, Mücke E. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 1990;9(1):66-104. doi:10.1145/77635.77639","mla":"Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” ACM Transactions on Graphics, vol. 9, no. 1, ACM, 1990, pp. 66–104, doi:10.1145/77635.77639."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_processing_charge":"No","publist_id":"2058","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Mücke","full_name":"Mücke, Ernst","first_name":"Ernst"}],"title":"Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms","publication_status":"published","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"language":[{"iso":"eng"}],"issue":"1","volume":9,"abstract":[{"lang":"eng","text":"This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software."}],"oa_version":"None","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/77635.77639"}],"scopus_import":"1","intvolume":" 9","month":"01","date_updated":"2022-02-22T14:58:39Z","extern":"1","_id":"4063","article_type":"original","type":"journal_article","status":"public"},{"abstract":[{"text":"This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra.","lang":"eng"}],"oa_version":"Published Version","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub"}],"scopus_import":"1","intvolume":" 10","month":"01","publication_status":"published","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"language":[{"iso":"eng"}],"issue":"3-4","volume":10,"_id":"4060","type":"journal_article","article_type":"original","status":"public","date_updated":"2022-02-23T10:10:35Z","extern":"1","acknowledgement":"Research of the first author is supported by Amoco Fnd. Fac. Dec. Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902, and research of the third author is supported in part by ONR Grant N00014-85K0570 and by NSF Grant DMS 8504322.","oa":1,"quality_controlled":"1","publisher":"Elsevier","year":"1990","publication":"Journal of Symbolic Computation","day":"01","page":"335 - 347","date_created":"2018-12-11T12:06:42Z","date_published":"1990-01-01T00:00:00Z","doi":"10.1016/S0747-7171(08)80068-5","citation":{"short":"H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347.","ieee":"H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” Journal of Symbolic Computation, vol. 10, no. 3–4. Elsevier, pp. 335–347, 1990.","apa":"Edelsbrunner, H., Preparata, F., & West, D. (1990). Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/S0747-7171(08)80068-5","ama":"Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 1990;10(3-4):335-347. doi:10.1016/S0747-7171(08)80068-5","mla":"Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” Journal of Symbolic Computation, vol. 10, no. 3–4, Elsevier, 1990, pp. 335–47, doi:10.1016/S0747-7171(08)80068-5.","ista":"Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347.","chicago":"Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” Journal of Symbolic Computation. Elsevier, 1990. https://doi.org/10.1016/S0747-7171(08)80068-5."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_processing_charge":"No","publist_id":"2061","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Preparata","full_name":"Preparata, Franco","first_name":"Franco"},{"last_name":"West","full_name":"West, Douglas","first_name":"Douglas"}],"title":"Tetrahedrizing point sets in three dimensions"},{"publist_id":"2060","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Arch","last_name":"Robison","full_name":"Robison, Arch"},{"full_name":"Shen, Xiao","last_name":"Shen","first_name":"Xiao"}],"article_processing_charge":"No","title":"Covering convex sets with non-overlapping polygons","citation":{"mla":"Edelsbrunner, Herbert, et al. “Covering Convex Sets with Non-Overlapping Polygons.” Discrete Mathematics, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:10.1016/0012-365X(90)90147-A.","ieee":"H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping polygons,” Discrete Mathematics, vol. 81, no. 2. Elsevier, pp. 153–164, 1990.","short":"H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164.","apa":"Edelsbrunner, H., Robison, A., & Shen, X. (1990). Covering convex sets with non-overlapping polygons. Discrete Mathematics. Elsevier. https://doi.org/10.1016/0012-365X(90)90147-A","ama":"Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 1990;81(2):153-164. doi:10.1016/0012-365X(90)90147-A","chicago":"Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets with Non-Overlapping Polygons.” Discrete Mathematics. Elsevier, 1990. https://doi.org/10.1016/0012-365X(90)90147-A.","ista":"Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 81(2), 153–164."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"153 - 164","date_published":"1990-04-15T00:00:00Z","doi":"10.1016/0012-365X(90)90147-A","date_created":"2018-12-11T12:06:44Z","year":"1990","day":"15","publication":"Discrete Mathematics","publisher":"Elsevier","quality_controlled":"1","acknowledgement":"The first author acknowledges the support by Amoco Fnd. Fat. Dev. Comput. Sci. l-6-44862. Work on this paper by the second author was supported by a Shell Fellowship in Computer Science. The third author as supported by the office of Naval Research under grant NOOO14-86K-0416. ","date_updated":"2022-02-22T15:45:55Z","extern":"1","article_type":"original","type":"journal_article","status":"public","_id":"4065","issue":"2","volume":81,"publication_identifier":{"eissn":["1872-681X"],"issn":["0012-365X"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub"}],"month":"04","intvolume":" 81","abstract":[{"text":"We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem.","lang":"eng"}],"oa_version":"None"},{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Clarkson, Kenneth, et al. “Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.” Discrete & Computational Geometry, vol. 5, no. 1, Springer, 1990, pp. 99–160, doi:10.1007/BF02187783.","ama":"Clarkson K, Edelsbrunner H, Guibas L, Sharir M, Welzl E. Combinatorial complexity bounds for arrangements of curves and spheres. Discrete & Computational Geometry. 1990;5(1):99-160. doi:10.1007/BF02187783","apa":"Clarkson, K., Edelsbrunner, H., Guibas, L., Sharir, M., & Welzl, E. (1990). Combinatorial complexity bounds for arrangements of curves and spheres. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187783","ieee":"K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, and E. Welzl, “Combinatorial complexity bounds for arrangements of curves and spheres,” Discrete & Computational Geometry, vol. 5, no. 1. Springer, pp. 99–160, 1990.","short":"K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, E. Welzl, Discrete & Computational Geometry 5 (1990) 99–160.","chicago":"Clarkson, Kenneth, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Emo Welzl. “Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.” Discrete & Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187783.","ista":"Clarkson K, Edelsbrunner H, Guibas L, Sharir M, Welzl E. 1990. Combinatorial complexity bounds for arrangements of curves and spheres. Discrete & Computational Geometry. 5(1), 99–160."},"title":"Combinatorial complexity bounds for arrangements of curves and spheres","publist_id":"2048","author":[{"last_name":"Clarkson","full_name":"Clarkson, Kenneth","first_name":"Kenneth"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Leonidas","last_name":"Guibas","full_name":"Guibas, Leonidas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"article_processing_charge":"No","acknowledgement":"The research of the second author was supported by the National Science Foundation under Grant CCR-8714565. Work by the fourth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation and the IBM Corporation, and by a research grant from the NCRD, the Israeli National Council for Research and Development. A preliminary version of this paper has appeared in theProceedings of the 29th IEEE Symposium on Foundations of Computer Science, 1988.","publisher":"Springer","quality_controlled":"1","day":"01","publication":"Discrete & Computational Geometry","year":"1990","date_published":"1990-03-01T00:00:00Z","doi":"10.1007/BF02187783","date_created":"2018-12-11T12:06:47Z","page":"99 - 160","_id":"4074","status":"public","article_type":"original","type":"journal_article","extern":"1","date_updated":"2022-02-17T15:41:04Z","oa_version":"None","abstract":[{"text":"We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike. For example, we prove that the maximum number of edges boundingm cells in an arrangement ofn lines is Θ(m 2/3 n 2/3 +n), and that it isO(m 2/3 n 2/3 β(n) +n) forn unit-circles, whereβ(n) (and laterβ(m, n)) is a function that depends on the inverse of Ackermann's function and grows extremely slowly. If we replace unit-circles by circles of arbitrary radii the upper bound goes up toO(m 3/5 n 4/5 β(n) +n). The same bounds (without theβ(n)-terms) hold for the maximum sum of degrees ofm vertices. In the case of vertex degrees in arrangements of lines and of unit-circles our bounds match previous results, but our proofs are considerably simpler than the previous ones. The maximum sum of degrees ofm vertices in an arrangement ofn spheres in three dimensions isO(m 4/7 n 9/7 β(m, n) +n 2), in general, andO(m 3/4 n 3/4 β(m, n) +n) if no three spheres intersect in a common circle. The latter bound implies that the maximum number of unit-distances amongm points in three dimensions isO(m 3/2 β(m)) which improves the best previous upper bound on this problem. Applications of our results to other distance problems are also given.","lang":"eng"}],"month":"03","intvolume":" 5","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187783"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","issue":"1","volume":5},{"year":"1990","publication_status":"published","publication_identifier":{"isbn":["978-0-89791-362-1"]},"language":[{"iso":"eng"}],"publication":"Proceedings of the 6th annual symposium on computational geometry","day":"01","page":"116 - 127","date_created":"2018-12-11T12:06:48Z","doi":"10.1145/98524.98551","date_published":"1990-01-01T00:00:00Z","abstract":[{"text":"In this paper we derived combinatorial point selection results for geometric objects defined by pairs of points. In a nutshell, the results say that if many pairs of a set of n points in some fixed dimension each define a geometric object of some type, then there is a point covered by many of these objects. Based on such a result for three-dimensional spheres we show that the combinatorial size of the Delaunay triangulation of a point set in space can be reduced by adding new points. We believe that from a practical point of view this is the most important result of this paper.","lang":"eng"}],"oa_version":"None","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98551"}],"quality_controlled":"1","publisher":"ACM","scopus_import":"1","month":"01","date_updated":"2022-02-17T10:09:54Z","citation":{"ama":"Chazelle B, Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M. Slimming down by adding; selecting heavily covered points. In: Proceedings of the 6th Annual Symposium on Computational Geometry. ACM; 1990:116-127. doi:10.1145/98524.98551","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., Hershberger, J., Seidel, R., & Sharir, M. (1990). Slimming down by adding; selecting heavily covered points. In Proceedings of the 6th annual symposium on computational geometry (pp. 116–127). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98551","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, M. Sharir, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 116–127.","ieee":"B. Chazelle, H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, and M. Sharir, “Slimming down by adding; selecting heavily covered points,” in Proceedings of the 6th annual symposium on computational geometry, Berkley, CA, United States, 1990, pp. 116–127.","mla":"Chazelle, Bernard, et al. “Slimming down by Adding; Selecting Heavily Covered Points.” Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 116–27, doi:10.1145/98524.98551.","ista":"Chazelle B, Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M. 1990. Slimming down by adding; selecting heavily covered points. Proceedings of the 6th annual symposium on computational geometry. SCG: Symposium on Computational Geometry, 116–127.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, John Hershberger, Raimund Seidel, and Micha Sharir. “Slimming down by Adding; Selecting Heavily Covered Points.” In Proceedings of the 6th Annual Symposium on Computational Geometry, 116–27. ACM, 1990. https://doi.org/10.1145/98524.98551."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","article_processing_charge":"No","author":[{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"first_name":"John","last_name":"Hershberger","full_name":"Hershberger, John"},{"first_name":"Raimund","full_name":"Seidel, Raimund","last_name":"Seidel"},{"last_name":"Sharir","full_name":"Sharir, Micha","first_name":"Micha"}],"publist_id":"2046","title":"Slimming down by adding; selecting heavily covered points","_id":"4078","conference":{"location":"Berkley, CA, United States","end_date":"1990-06-09","start_date":"1990-06-07","name":"SCG: Symposium on Computational Geometry"},"type":"conference","status":"public"},{"scopus_import":"1","quality_controlled":"1","publisher":"ACM","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98567"}],"month":"01","abstract":[{"text":"We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3, which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in E3.","lang":"eng"}],"oa_version":"None","page":"203 - 210","doi":"10.1145/98524.98567","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:06:48Z","publication_identifier":{"isbn":["978-0-89791-362-1"]},"year":"1990","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"Proceedings of the 6th annual symposium on Computational geometry","type":"conference","conference":{"start_date":"1990-06-07","location":"Berkeley, CA, United States","end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry"},"status":"public","_id":"4076","author":[{"full_name":"Agarwal, Pankaj","last_name":"Agarwal","first_name":"Pankaj"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Schwarzkopf","full_name":"Schwarzkopf, Otfried","first_name":"Otfried"},{"last_name":"Welzl","full_name":"Welzl, Emo","first_name":"Emo"}],"publist_id":"2044","article_processing_charge":"No","title":" Euclidean minimum spanning trees and bichromatic closest pairs","date_updated":"2022-02-16T15:30:22Z","citation":{"mla":"Agarwal, Pankaj, et al. “ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–10, doi:10.1145/98524.98567.","apa":"Agarwal, P., Edelsbrunner, H., Schwarzkopf, O., & Welzl, E. (1990). Euclidean minimum spanning trees and bichromatic closest pairs. In Proceedings of the 6th annual symposium on Computational geometry (pp. 203–210). Berkeley, CA, United States: ACM. https://doi.org/10.1145/98524.98567","ama":"Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. Euclidean minimum spanning trees and bichromatic closest pairs. In: Proceedings of the 6th Annual Symposium on Computational Geometry. ACM; 1990:203-210. doi:10.1145/98524.98567","ieee":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, and E. Welzl, “ Euclidean minimum spanning trees and bichromatic closest pairs,” in Proceedings of the 6th annual symposium on Computational geometry, Berkeley, CA, United States, 1990, pp. 203–210.","short":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210.","chicago":"Agarwal, Pankaj, Herbert Edelsbrunner, Otfried Schwarzkopf, and Emo Welzl. “ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” In Proceedings of the 6th Annual Symposium on Computational Geometry, 203–10. ACM, 1990. https://doi.org/10.1145/98524.98567.","ista":"Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. 1990. Euclidean minimum spanning trees and bichromatic closest pairs. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 203–210."},"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17"},{"citation":{"mla":"Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 112–15, doi:10.1145/98524.98548.","apa":"Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., & Wenger, R. (1990). Points and triangles in the plane and halving planes in space. In Proceedings of the 6th annual symposium on Computational geometry (pp. 112–115). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98548","ama":"Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. In: Proceedings of the 6th Annual Symposium on Computational Geometry. ACM; 1990:112-115. doi:10.1145/98524.98548","short":"B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 112–115.","ieee":"B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger, “Points and triangles in the plane and halving planes in space,” in Proceedings of the 6th annual symposium on Computational geometry, Berkley, CA, United States, 1990, pp. 112–115.","chicago":"Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving Planes in Space.” In Proceedings of the 6th Annual Symposium on Computational Geometry, 112–15. ACM, 1990. https://doi.org/10.1145/98524.98548.","ista":"Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990. Points and triangles in the plane and halving planes in space. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 112–115."},"date_updated":"2022-02-17T09:42:27Z","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"first_name":"Boris","last_name":"Aronov","full_name":"Aronov, Boris"},{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Guibas","full_name":"Guibas, Leonidas","first_name":"Leonidas"},{"last_name":"Sharir","full_name":"Sharir, Micha","first_name":"Micha"},{"first_name":"Rephael","last_name":"Wenger","full_name":"Wenger, Rephael"}],"publist_id":"2045","article_processing_charge":"No","title":"Points and triangles in the plane and halving planes in space","_id":"4077","type":"conference","conference":{"start_date":"1990-06-07","location":"Berkley, CA, United States","end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry"},"status":"public","publication_identifier":{"isbn":["978-0-89791-362-1"]},"publication_status":"published","year":"1990","day":"01","publication":"Proceedings of the 6th annual symposium on Computational geometry","language":[{"iso":"eng"}],"page":"112 - 115","doi":"10.1145/98524.98548","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:06:48Z","abstract":[{"text":"We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.","lang":"eng"}],"oa_version":"None","quality_controlled":"1","scopus_import":"1","publisher":"ACM","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98548"}],"month":"01"},{"page":"561 - 571","date_created":"2018-12-11T12:06:47Z","date_published":"1990-06-01T00:00:00Z","doi":"10.1007/BF01840404","year":"1990","publication":"Algorithmica","day":"01","publisher":"Springer","quality_controlled":"1","acknowledgement":"The first author is pleased to acknowledge support by the National Science Foundation under Grant CCR-8700917. The research of the second author was supported by Amoco Foundation Faculty Development Grant CS 1-6-44862 and by the National Science Foundatio","article_processing_charge":"No","publist_id":"2049","author":[{"last_name":"Dobkin","full_name":"Dobkin, David","first_name":"David"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Overmars","full_name":"Overmars, Mark","first_name":"Mark"}],"title":"Searching for empty convex polygons","citation":{"mla":"Dobkin, David, et al. “Searching for Empty Convex Polygons.” Algorithmica, vol. 5, no. 4, Springer, 1990, pp. 561–71, doi:10.1007/BF01840404.","ieee":"D. Dobkin, H. Edelsbrunner, and M. Overmars, “Searching for empty convex polygons,” Algorithmica, vol. 5, no. 4. Springer, pp. 561–571, 1990.","short":"D. Dobkin, H. Edelsbrunner, M. Overmars, Algorithmica 5 (1990) 561–571.","apa":"Dobkin, D., Edelsbrunner, H., & Overmars, M. (1990). Searching for empty convex polygons. Algorithmica. Springer. https://doi.org/10.1007/BF01840404","ama":"Dobkin D, Edelsbrunner H, Overmars M. Searching for empty convex polygons. Algorithmica. 1990;5(4):561-571. doi:10.1007/BF01840404","chicago":"Dobkin, David, Herbert Edelsbrunner, and Mark Overmars. “Searching for Empty Convex Polygons.” Algorithmica. Springer, 1990. https://doi.org/10.1007/BF01840404.","ista":"Dobkin D, Edelsbrunner H, Overmars M. 1990. Searching for empty convex polygons. Algorithmica. 5(4), 561–571."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","issue":"4","volume":5,"publication_status":"published","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01840404"}],"scopus_import":"1","intvolume":" 5","month":"06","abstract":[{"text":"A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r> 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.","lang":"eng"}],"oa_version":"None","date_updated":"2022-02-21T10:55:13Z","extern":"1","article_type":"original","type":"journal_article","status":"public","_id":"4075"},{"month":"01","quality_controlled":"1","publisher":"Springer","main_file_link":[{"url":"https://link.springer.com/book/10.1007/978-3-642-74474-7"}],"oa_version":"None","date_published":"1990-01-01T00:00:00Z","doi":"10.1007/978-3-642-74474-7_5","date_created":"2018-12-11T12:08:11Z","page":"115 - 174","day":"01","language":[{"iso":"eng"}],"publication":"Population biology: Ecological and evolutionary viewpoints","publication_identifier":{"isbn":[" 978-3642744761"]},"year":"1990","publication_status":"published","status":"public","type":"book_chapter","_id":"4311","editor":[{"first_name":"Klaus","full_name":"Wöhrmann, Klaus","last_name":"Wöhrmann"},{"full_name":"Jain, Subodh","last_name":"Jain","first_name":"Subodh"}],"title":"Population structure and processes in evolution","author":[{"orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","last_name":"Barton","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H"},{"first_name":"A.","full_name":"Clark, A.","last_name":"Clark"}],"publist_id":"1748","article_processing_charge":"No","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"ista":"Barton NH, Clark A. 1990.Population structure and processes in evolution. In: Population biology: Ecological and evolutionary viewpoints. , 115–174.","chicago":"Barton, Nicholas H, and A. Clark. “Population Structure and Processes in Evolution.” In Population Biology: Ecological and Evolutionary Viewpoints, edited by Klaus Wöhrmann and Subodh Jain, 115–74. Springer, 1990. https://doi.org/10.1007/978-3-642-74474-7_5.","ama":"Barton NH, Clark A. Population structure and processes in evolution. In: Wöhrmann K, Jain S, eds. Population Biology: Ecological and Evolutionary Viewpoints. Springer; 1990:115-174. doi:10.1007/978-3-642-74474-7_5","apa":"Barton, N. H., & Clark, A. (1990). Population structure and processes in evolution. In K. Wöhrmann & S. Jain (Eds.), Population biology: Ecological and evolutionary viewpoints (pp. 115–174). Springer. https://doi.org/10.1007/978-3-642-74474-7_5","ieee":"N. H. Barton and A. Clark, “Population structure and processes in evolution,” in Population biology: Ecological and evolutionary viewpoints, K. Wöhrmann and S. Jain, Eds. Springer, 1990, pp. 115–174.","short":"N.H. Barton, A. Clark, in:, K. Wöhrmann, S. Jain (Eds.), Population Biology: Ecological and Evolutionary Viewpoints, Springer, 1990, pp. 115–174.","mla":"Barton, Nicholas H., and A. Clark. “Population Structure and Processes in Evolution.” Population Biology: Ecological and Evolutionary Viewpoints, edited by Klaus Wöhrmann and Subodh Jain, Springer, 1990, pp. 115–74, doi:10.1007/978-3-642-74474-7_5."},"date_updated":"2022-02-16T10:49:05Z"},{"page":"415 - 416","date_created":"2018-12-11T12:08:11Z","doi":"10.1038/346415a0","date_published":"1990-08-02T00:00:00Z","volume":346,"publication_status":"published","year":"1990","publication_identifier":{"eissn":["1476-4687"],"issn":["0028-0836"]},"publication":"Nature","language":[{"iso":"eng"}],"day":"02","main_file_link":[{"url":"https://www.nature.com/articles/346415a0"}],"quality_controlled":"1","scopus_import":"1","publisher":"Nature Publishing Group","intvolume":" 346","month":"08","oa_version":"None","article_processing_charge":"No","author":[{"first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","last_name":"Barton"},{"first_name":"Steve","full_name":"Jones, Steve","last_name":"Jones"}],"publist_id":"1749","title":"The language of the genes","citation":{"chicago":"Barton, Nicholas H, and Steve Jones. “The Language of the Genes.” Nature. Nature Publishing Group, 1990. https://doi.org/10.1038/346415a0.","ista":"Barton NH, Jones S. 1990. The language of the genes. Nature. 346, 415–416.","mla":"Barton, Nicholas H., and Steve Jones. “The Language of the Genes.” Nature, vol. 346, Nature Publishing Group, 1990, pp. 415–16, doi:10.1038/346415a0.","apa":"Barton, N. H., & Jones, S. (1990). The language of the genes. Nature. Nature Publishing Group. https://doi.org/10.1038/346415a0","ama":"Barton NH, Jones S. The language of the genes. Nature. 1990;346:415-416. doi:10.1038/346415a0","ieee":"N. H. Barton and S. Jones, “The language of the genes,” Nature, vol. 346. Nature Publishing Group, pp. 415–416, 1990.","short":"N.H. Barton, S. Jones, Nature 346 (1990) 415–416."},"date_updated":"2022-02-16T10:51:50Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","type":"journal_article","article_type":"original","status":"public","_id":"4310"},{"title":"An interleaving model for real time","article_processing_charge":"No","publist_id":"220","author":[{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","orcid":"0000−0002−2985−7724","full_name":"Henzinger, Thomas A","last_name":"Henzinger"},{"first_name":"Zohar","full_name":"Manna, Zohar","last_name":"Manna"},{"first_name":"Amir","last_name":"Pnueli","full_name":"Pnueli, Amir"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","date_updated":"2022-02-15T15:51:25Z","citation":{"ista":"Henzinger TA, Manna Z, Pnueli A. 1990. An interleaving model for real time. Proceedings of the 5th Jerusalem Conference on Information Technology. JCIT: Jerusalem Conference on Information Technology, 717–730.","chicago":"Henzinger, Thomas A, Zohar Manna, and Amir Pnueli. “An Interleaving Model for Real Time.” In Proceedings of the 5th Jerusalem Conference on Information Technology, 717–30. IEEE, 1990. https://doi.org/10.1109/JCIT.1990.128356.","ama":"Henzinger TA, Manna Z, Pnueli A. An interleaving model for real time. In: Proceedings of the 5th Jerusalem Conference on Information Technology. IEEE; 1990:717-730. doi:10.1109/JCIT.1990.128356","apa":"Henzinger, T. A., Manna, Z., & Pnueli, A. (1990). An interleaving model for real time. In Proceedings of the 5th Jerusalem Conference on Information Technology (pp. 717–730). Jerusalem, Israel: IEEE. https://doi.org/10.1109/JCIT.1990.128356","ieee":"T. A. Henzinger, Z. Manna, and A. Pnueli, “An interleaving model for real time,” in Proceedings of the 5th Jerusalem Conference on Information Technology, Jerusalem, Israel, 1990, pp. 717–730.","short":"T.A. Henzinger, Z. Manna, A. Pnueli, in:, Proceedings of the 5th Jerusalem Conference on Information Technology, IEEE, 1990, pp. 717–730.","mla":"Henzinger, Thomas A., et al. “An Interleaving Model for Real Time.” Proceedings of the 5th Jerusalem Conference on Information Technology, IEEE, 1990, pp. 717–30, doi:10.1109/JCIT.1990.128356."},"status":"public","conference":{"end_date":"1990-10-25","location":"Jerusalem, Israel","start_date":"1990-10-22","name":"JCIT: Jerusalem Conference on Information Technology"},"type":"conference","_id":"4510","date_created":"2018-12-11T12:09:14Z","doi":"10.1109/JCIT.1990.128356","date_published":"1990-01-01T00:00:00Z","page":"717 - 730","language":[{"iso":"eng"}],"publication":" Proceedings of the 5th Jerusalem Conference on Information Technology","day":"01","publication_status":"published","year":"1990","publication_identifier":{"isbn":["0-8186-2078-1"]},"month":"01","main_file_link":[{"url":"https://ieeexplore.ieee.org/abstract/document/128356"}],"publisher":"IEEE","quality_controlled":"1","scopus_import":"1","acknowledgement":"Sponsors: IBM graduate fellowship, National Science Foundation grant CCR-89-11512, National Science Foundation CCR-89-13641, Defense Advanced Research Projects Agency under contract N00039-84-C-0211, United States Air Force Office of Scientific Research under contract AFOSR-90-0057, European Community ESPRIT Basic Research Action project 3096 (SPEC).","oa_version":"None","abstract":[{"text":"The interleaving model is both adequate and sufficiently abstract to allow for the practical specification and verification of many properties of concurrent systems. We incorporate real time into this model by defining the abstract notion of a real-time transition system as a conservative extension of traditional transition systems: qualitative fairness requirements are replaced (and superseded) by quantitative lower-bound and upper-bound real-time requirements for transitions.\r\nWe present proof rules to establish lower and upper real-time bounds for response properties of real-time transition systems. This proof system can be used to verify bounded-invariance and bounded-response properties, such as timely termination of shared-variables multi-process systems, whose semantics is defined in terms of real-time transition systems.","lang":"eng"}]},{"day":"01","language":[{"iso":"eng"}],"publication":"Proceedings of the 9th annual ACM symposium on Principles of distributed computing","publication_identifier":{"isbn":["978-0-89791-404-8"]},"year":"1990","publication_status":"published","doi":"10.1145/93385.93429","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:09:17Z","page":"281 - 296","oa_version":"None","acknowledgement":"Many thanks to Rajeev Alur, Adam Grove, Zohar Manna, and Amir Pnueli for their continuous discussions and support.","abstract":[{"text":"We introduce a novel extension of propositional modal logic that is interpreted over Kripke structures in which a value is associated with every possible world. These values are. however, not treated as full first-order objects: they can be accessed only by a very restricted form of quantification: the \"freeze\" quantifier binds a variable to the value of the current world. We present a complete proof system for this (\"half-order\") modal logic. As a special case, we obtain the real-time temporal logic TPTL of [AH891: the models are restricted to infinite sequences of states, whose values are monotonically increasing natural numbers. The ordering relation between states is interpreted as temporal precedence. while the value associated with a state is interpreted as its \"rear time. We extend our proof system to be complete for TPTL. and demonstrate how it can be used to derive real-time properties. ","lang":"eng"}],"month":"01","publisher":"ACM","scopus_import":"1","quality_controlled":"1","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/93385.93429"}],"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Henzinger, Thomas A. “Half-Order Modal Logic: How to Prove Real-Time Properties.” Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing, ACM, 1990, pp. 281–96, doi:10.1145/93385.93429.","apa":"Henzinger, T. A. (1990). Half-order modal logic: How to prove real-time properties. In Proceedings of the 9th annual ACM symposium on Principles of distributed computing (pp. 281–296). Quebec City, Canada: ACM. https://doi.org/10.1145/93385.93429","ama":"Henzinger TA. Half-order modal logic: How to prove real-time properties. In: Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing. ACM; 1990:281-296. doi:10.1145/93385.93429","short":"T.A. Henzinger, in:, Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing, ACM, 1990, pp. 281–296.","ieee":"T. A. Henzinger, “Half-order modal logic: How to prove real-time properties,” in Proceedings of the 9th annual ACM symposium on Principles of distributed computing, Quebec City, Canada, 1990, pp. 281–296.","chicago":"Henzinger, Thomas A. “Half-Order Modal Logic: How to Prove Real-Time Properties.” In Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing, 281–96. ACM, 1990. https://doi.org/10.1145/93385.93429.","ista":"Henzinger TA. 1990. Half-order modal logic: How to prove real-time properties. Proceedings of the 9th annual ACM symposium on Principles of distributed computing. PODC: Principles of Distributed Computing, 281–296."},"date_updated":"2022-02-15T15:11:03Z","title":"Half-order modal logic: How to prove real-time properties","publist_id":"209","author":[{"first_name":"Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","orcid":"0000−0002−2985−7724","full_name":"Henzinger, Thomas A"}],"article_processing_charge":"No","_id":"4522","status":"public","type":"conference","conference":{"name":"PODC: Principles of Distributed Computing","start_date":"1990-08-22","location":"Quebec City, Canada","end_date":"1990-08-24"}},{"day":"06","language":[{"iso":"eng"}],"publication":" 5th Annual IEEE Symposium on Logic in Computer Science","publication_identifier":{"isbn":["0-8186-2073-0"]},"year":"1990","publication_status":"published","doi":"10.1109/LICS.1990.113764","date_published":"1990-08-06T00:00:00Z","date_created":"2018-12-11T12:09:40Z","page":"390 - 401","oa_version":"None","abstract":[{"text":"A unifying framework for the study of real-time logics is developed. In analogy to the untimed case, the underlying classical theory of timed state sequences is identified, it is shown to be nonelementarily decidable, and its complexity and expressiveness are used as a point of reference. Two orthogonal extensions of PTL (timed propositional temporal logic and metric temporal logic) that inherit its appeal are defined: they capture elementary, yet expressively complete, fragments of the theory of timed state sequences, and thus are excellent candidates for practical real-time specification languages","lang":"eng"}],"month":"08","quality_controlled":"1","scopus_import":"1","publisher":"IEEE","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/113764"}],"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Alur, Rajeev, and Thomas A. Henzinger. “Real-Time Logics: Complexity and Expressiveness.” 5th Annual IEEE Symposium on Logic in Computer Science, IEEE, 1990, pp. 390–401, doi:10.1109/LICS.1990.113764.","ama":"Alur R, Henzinger TA. Real-time logics: Complexity and expressiveness. In: 5th Annual IEEE Symposium on Logic in Computer Science. IEEE; 1990:390-401. doi:10.1109/LICS.1990.113764","apa":"Alur, R., & Henzinger, T. A. (1990). Real-time logics: Complexity and expressiveness. In 5th Annual IEEE Symposium on Logic in Computer Science (pp. 390–401). Philadelphia, PA, USA: IEEE. https://doi.org/10.1109/LICS.1990.113764","short":"R. Alur, T.A. Henzinger, in:, 5th Annual IEEE Symposium on Logic in Computer Science, IEEE, 1990, pp. 390–401.","ieee":"R. Alur and T. A. Henzinger, “Real-time logics: Complexity and expressiveness,” in 5th Annual IEEE Symposium on Logic in Computer Science, Philadelphia, PA, USA, 1990, pp. 390–401.","chicago":"Alur, Rajeev, and Thomas A Henzinger. “Real-Time Logics: Complexity and Expressiveness.” In 5th Annual IEEE Symposium on Logic in Computer Science, 390–401. IEEE, 1990. https://doi.org/10.1109/LICS.1990.113764.","ista":"Alur R, Henzinger TA. 1990. Real-time logics: Complexity and expressiveness. 5th Annual IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 390–401."},"date_updated":"2022-02-15T14:35:30Z","title":"Real-time logics: Complexity and expressiveness","author":[{"last_name":"Alur","full_name":"Alur, Rajeev","first_name":"Rajeev"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","full_name":"Henzinger, Thomas A","orcid":"0000−0002−2985−7724","last_name":"Henzinger"}],"publist_id":"112","article_processing_charge":"No","_id":"4597","status":"public","type":"conference","conference":{"name":"LICS: Logic in Computer Science","start_date":"1990-06-04","end_date":"1990-06-07","location":"Philadelphia, PA, USA"}}]