[{"extern":"1","abstract":[{"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.","lang":"eng"}],"publist_id":"2047","type":"conference","date_created":"2018-12-11T12:06:47Z","date_updated":"2022-02-17T11:07:07Z","oa_version":"None","author":[{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"full_name":"Pollack, Richard","last_name":"Pollack","first_name":"Richard"},{"full_name":"Seidel, Raimund","first_name":"Raimund","last_name":"Seidel"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"full_name":"Snoeyink, Jack","last_name":"Snoeyink","first_name":"Jack"}],"status":"public","title":"Counting and cutting cycles of lines and rods in space","publication_status":"published","publisher":"IEEE","_id":"4073","year":"1990","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","month":"01","day":"01","article_processing_charge":"No","publication_identifier":{"isbn":["0-8186-2082-X"]},"scopus_import":"1","language":[{"iso":"eng"}],"conference":{"end_date":"1990-10-24","location":"St. Louis, MO, United States of America","start_date":"1990-10-22","name":"FOCS: Foundations of Computer Science"},"doi":"10.1109/FSCS.1990.89543","date_published":"1990-01-01T00:00:00Z","quality_controlled":"1","page":"242 - 251","publication":"31st Annual Symposium on Foundations of Computer Science","citation":{"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.","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.","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.","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."},"main_file_link":[{"url":"https://ieeexplore.ieee.org/document/89543"}]},{"date_published":"1990-01-01T00:00:00Z","page":"129 - 144","publication":"International Journal of Computer Mathematics","citation":{"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","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.","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.","apa":"Edelsbrunner, H., Overmars, M., Welzl, E., Hartman, I., & Feldman, J. (1990). Ranking intervals under visibility constraints. International Journal of Computer Mathematics. Taylor & Francis. https://doi.org/10.1080/00207169008803871","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.","short":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International Journal of Computer Mathematics 34 (1990) 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."},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"None","title":"Ranking intervals under visibility constraints","status":"public","intvolume":" 34","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4070","abstract":[{"lang":"eng","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)
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.","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.","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","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.","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.","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"},"publication":"Proceedings of the 6th annual symposium on Computational geometry","language":[{"iso":"eng"}],"doi":"10.1145/98524.98535","date_published":"1990-01-01T00:00:00Z","conference":{"name":"SCG: Symposium on Computational Geometry","start_date":"1990-06-07","location":"Berkley, CA, United States","end_date":"1990-06-09"},"article_processing_charge":"No","publication_identifier":{"isbn":["978-0-89791-362-1"]},"month":"01","day":"01"},{"year":"1990","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","publication_status":"published","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"volume":5,"date_created":"2018-12-11T12:06:45Z","date_updated":"2022-02-22T14:50:34Z","publist_id":"2057","extern":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187778"}],"quality_controlled":"1","doi":"10.1007/BF02187778","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4068","intvolume":" 5","title":"The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2","status":"public","oa_version":"None","type":"journal_article","issue":"1","abstract":[{"lang":"eng","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."}],"citation":{"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.","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.","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.","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","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.","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"},"publication":"Discrete & Computational Geometry","page":"35 - 42","article_type":"original","date_published":"1990-01-01T00:00:00Z","article_processing_charge":"No","day":"01"},{"date_published":"1990-09-01T00:00:00Z","article_type":"original","page":"251 - 260","publication":"Combinatorica","citation":{"ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 1990;10(3):251-260. doi:10.1007/BF02122779","ista":"Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260.","apa":"Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. Combinatorica. Springer. https://doi.org/10.1007/BF02122779","ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” Combinatorica, vol. 10, no. 3. Springer, pp. 251–260, 1990.","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.","chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” Combinatorica. Springer, 1990. https://doi.org/10.1007/BF02122779."},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"None","status":"public","title":"An acyclicity theorem for cell complexes in d dimension","intvolume":" 10","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4069","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"}],"issue":"3","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/BF02122779","quality_controlled":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02122779"}],"month":"09","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"date_updated":"2022-02-21T11:08:30Z","date_created":"2018-12-11T12:06:45Z","volume":10,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"publication_status":"published","publisher":"Springer","year":"1990","acknowledgement":"Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565.","extern":"1","publist_id":"2050"},{"oa_version":"None","title":"A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments","status":"public","intvolume":" 420","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"3467","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."}],"type":"journal_article","date_published":"1990-01-01T00:00:00Z","article_type":"original","page":"365 - 385","publication":"Journal of Physiology","citation":{"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.","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.","short":"M. Bräu, F. Dreyer, P.M. Jonas, H. Repp, W. Vogel, Journal of Physiology 420 (1990) 365–385.","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.","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","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.","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"},"day":"01","article_processing_charge":"No","scopus_import":"1","date_created":"2018-12-11T12:03:29Z","date_updated":"2022-02-23T16:10:03Z","volume":420,"author":[{"full_name":"Bräu, Michael","last_name":"Bräu","first_name":"Michael"},{"first_name":"Florian","last_name":"Dreyer","full_name":"Dreyer, Florian"},{"first_name":"Peter M","last_name":"Jonas","id":"353C1B58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5001-4804","full_name":"Jonas, Peter M"},{"full_name":"Repp, Holger","first_name":"Holger","last_name":"Repp"},{"full_name":"Vogel, Werner","first_name":"Werner","last_name":"Vogel"}],"publication_status":"published","publisher":"Wiley-Blackwell","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","year":"1990","pmid":1,"extern":"1","publist_id":"2920","language":[{"iso":"eng"}],"doi":"10.1113/jphysiol.1990.sp017918","quality_controlled":"1","main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1190055/","open_access":"1"}],"oa":1,"external_id":{"pmid":["2324990"]},"month":"01","publication_identifier":{"eissn":["1469-7793"],"issn":["0022-3751"]}},{"date_updated":"2022-02-23T15:41:07Z","date_created":"2018-12-11T12:03:59Z","oa_version":"None","author":[{"full_name":"Dobkin, David","last_name":"Dobkin","first_name":"David"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Yap","first_name":"Chee","full_name":"Yap, Chee"}],"title":"Probing convex polytopes","status":"public","publication_status":"published","publisher":"Springer","editor":[{"first_name":"Ingemar","last_name":"Cox","full_name":"Cox, Ingemar"},{"first_name":"Gordon","last_name":"Wilfong","full_name":"Wilfong, Gordon"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"3565","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","year":"1990","extern":"1","abstract":[{"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.","lang":"eng"}],"publist_id":"2820","type":"book_chapter","language":[{"iso":"eng"}],"doi":"10.1007/978-1-4613-8997-2_25","date_published":"1990-01-01T00:00:00Z","quality_controlled":"1","page":"328 - 341","publication":"Autonomous Robot Vehicles","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-1-4613-8997-2_25"}],"citation":{"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","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.","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","ista":"Dobkin D, Edelsbrunner H, Yap C. 1990.Probing convex polytopes. In: Autonomous Robot Vehicles. , 328–341.","short":"D. Dobkin, H. Edelsbrunner, C. Yap, in:, I. Cox, G. Wilfong (Eds.), Autonomous Robot Vehicles, Springer, 1990, pp. 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.","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."},"day":"01","month":"01","publication_identifier":{"isbn":["978-1-4613-8997-2"]},"article_processing_charge":"No"},{"publist_id":"2059","extern":"1","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Souvaine","first_name":"Diane","full_name":"Souvaine, Diane"}],"date_created":"2018-12-11T12:06:43Z","date_updated":"2022-02-22T15:10:54Z","volume":85,"year":"1990","publication_status":"published","publisher":"American Statistical Association","month":"01","publication_identifier":{"eissn":["1537-274X"],"issn":["0003-1291"]},"doi":"10.1080/01621459.1990.10475313","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10475313"}],"quality_controlled":"1","abstract":[{"lang":"eng","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."}],"issue":"409","type":"journal_article","oa_version":"None","_id":"4064","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","title":"Computing least median of squares regression lines and guided topological sweep","intvolume":" 85","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"1990-01-01T00:00:00Z","publication":"Journal of the American Statistical Association","citation":{"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","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","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.","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.","short":"H. Edelsbrunner, D. Souvaine, Journal of the American Statistical Association 85 (1990) 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.","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."},"article_type":"original","page":"115 - 119"},{"publist_id":"2058","extern":"1","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Mücke","first_name":"Ernst","full_name":"Mücke, Ernst"}],"date_created":"2018-12-11T12:06:43Z","date_updated":"2022-02-22T14:58:39Z","volume":9,"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. ","year":"1990","publication_status":"published","publisher":"ACM","month":"01","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"doi":"10.1145/77635.77639","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/77635.77639"}],"quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"issue":"1","type":"journal_article","oa_version":"None","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4063","status":"public","title":"Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms","intvolume":" 9","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"1990-01-01T00:00:00Z","publication":"ACM Transactions on Graphics","citation":{"short":"H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 9 (1990) 66–104.","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.","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.","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","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","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.","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."},"article_type":"original","page":"66 - 104"},{"date_published":"1990-01-01T00:00:00Z","citation":{"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","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","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.","ista":"Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347.","short":"H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347.","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.","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."},"publication":"Journal of Symbolic Computation","page":"335 - 347","article_type":"original","article_processing_charge":"No","day":"01","scopus_import":"1","oa_version":"Published Version","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4060","intvolume":" 10","title":"Tetrahedrizing point sets in three dimensions","status":"public","issue":"3-4","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"}],"type":"journal_article","doi":"10.1016/S0747-7171(08)80068-5","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub"}],"quality_controlled":"1","publication_identifier":{"eissn":["1095-855X"],"issn":["0747-7171"]},"month":"01","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Preparata, Franco","last_name":"Preparata","first_name":"Franco"},{"full_name":"West, Douglas","last_name":"West","first_name":"Douglas"}],"volume":10,"date_created":"2018-12-11T12:06:42Z","date_updated":"2022-02-23T10:10:35Z","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.","year":"1990","publisher":"Elsevier","publication_status":"published","publist_id":"2061","extern":"1"}]