[{"series_title":"SpringerBriefs in Applied Sciences and Technology","scopus_import":"1","publication_identifier":{"isbn":["9-783-3190-5956-3"],"eissn":["2191-5318"],"issn":["2191-530X"],"eisbn":["9-783-3190-5957-0"]},"article_processing_charge":"No","month":"01","day":"01","page":"IX, 110","quality_controlled":"1","citation":{"chicago":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.","mla":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0.","short":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014.","ista":"Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.","apa":"Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology (1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0","ieee":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.","ama":"Edelsbrunner H. A Short Course in Computational Geometry and Topology. 1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0"},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-05957-0","date_published":"2014-01-01T00:00:00Z","place":"Cham","alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"type":"book","abstract":[{"lang":"eng","text":"This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields."}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","title":"A Short Course in Computational Geometry and Topology","publication_status":"published","status":"public","_id":"6853","year":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","date_created":"2019-09-06T09:22:33Z","date_updated":"2022-03-04T07:47:54Z","related_material":{"link":[{"relation":"other","description":"available as eBook via catalog IST BookList","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106"},{"description":"available via catalog IST BookList","relation":"other","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842"}]},"edition":"1","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}]},{"type":"conference","alternative_title":["Mathematics and Visualization"],"abstract":[{"lang":"eng","text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set."}],"year":"2014","_id":"10886","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","status":"public","author":[{"full_name":"Zobel, Valentin","last_name":"Zobel","first_name":"Valentin"},{"last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"}],"oa_version":"None","date_created":"2022-03-18T13:05:39Z","date_updated":"2023-09-05T14:13:16Z","scopus_import":"1","article_processing_charge":"No","publication_identifier":{"eisbn":["9783319040998"],"issn":["1612-3786"],"eissn":["2197-666X"],"isbn":["9783319040981"]},"month":"03","day":"19","citation":{"ama":"Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: Topological Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In Topological Methods in Data Analysis and Visualization III (pp. 249–262). Springer. https://doi.org/10.1007/978-3-319-04099-8_16","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in Topological Methods in Data Analysis and Visualization III , 2014, pp. 249–262.","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In Topological Methods in Data Analysis and Visualization III , 249–62. 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Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption."}],"citation":{"short":"D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.","mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9.","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.","ama":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9","ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in Topological Methods in Data Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.","ista":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150."},"publication":"Topological Methods in Data Analysis and Visualization III.","page":"135-150","date_published":"2014-03-19T00:00:00Z","scopus_import":"1","series_title":"Mathematics and Visualization","article_processing_charge":"No","day":"19"},{"month":"09","publication_identifier":{"issn":["09249907"]},"quality_controlled":"1","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s10851-013-0468-x","file_date_updated":"2020-07-14T12:45:35Z","publist_id":"4691","ec_funded":1,"publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"year":"2014","date_created":"2018-12-11T11:56:36Z","date_updated":"2023-09-07T11:41:25Z","volume":50,"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian"}],"related_material":{"record":[{"id":"2843","status":"public","relation":"earlier_version"},{"relation":"dissertation_contains","status":"public","id":"1399"}]},"scopus_import":1,"day":"01","has_accepted_license":"1","page":"164 - 177","publication":"Journal of Mathematical Imaging and Vision","citation":{"ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x","ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","apa":"Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.","short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer, 2014. https://doi.org/10.1007/s10851-013-0468-x."},"date_published":"2014-09-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm."}],"issue":"1","title":"Stable length estimates of tube-like shapes","status":"public","ddc":["000"],"intvolume":" 50","_id":"2255","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","file":[{"access_level":"open_access","file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","file_size":3941391,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5204","checksum":"2f93f3e63a38a85cd4404d7953913b14","date_updated":"2020-07-14T12:45:35Z","date_created":"2018-12-12T10:16:18Z"}],"pubrep_id":"549"},{"scopus_import":"1","series_title":"LNCS","article_processing_charge":"No","day":"01","citation":{"ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software. ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_24","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: ICMS 2014: International Congress on Mathematical Software. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:10.1007/978-3-662-44199-2_24","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24.","mla":"Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS 2014: International Congress on Mathematical Software, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143."},"publication":"ICMS 2014: International Congress on Mathematical Software","page":"137-143","date_published":"2014-09-01T00:00:00Z","type":"conference","abstract":[{"lang":"eng","text":"PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10894","intvolume":" 8592","status":"public","title":"PHAT – Persistent Homology Algorithms Toolbox","oa_version":"None","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783662441985"],"eisbn":["9783662441992"],"issn":["0302-9743"]},"month":"09","quality_controlled":"1","doi":"10.1007/978-3-662-44199-2_24","conference":{"name":"ICMS: International Congress on Mathematical Software","end_date":"2014-08-09","start_date":"2014-08-05","location":"Seoul, South Korea"},"language":[{"iso":"eng"}],"place":"Berlin, Heidelberg","year":"2014","department":[{"_id":"HeEd"}],"publisher":"Springer Berlin Heidelberg","publication_status":"published","related_material":{"record":[{"id":"1433","relation":"later_version","status":"public"}]},"author":[{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert"}],"volume":8592,"date_updated":"2023-09-20T09:42:40Z","date_created":"2022-03-21T07:12:16Z"},{"main_file_link":[{"open_access":"1","url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf"}],"citation":{"chicago":"Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.).","ista":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.","ieee":"M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. .","apa":"Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468","ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/arXiv.1401.0468"},"oa":1,"external_id":{"arxiv":["1401.0468"]},"publication":"arXiv","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.1401.0468","date_published":"2014-01-01T00:00:00Z","article_processing_charge":"No","month":"01","day":"01","department":[{"_id":"HeEd"},{"_id":"CaUh"}],"publication_status":"submitted","title":"Sphere packing with limited overlap","status":"public","_id":"2012","year":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper. The second author has been supported by the Max Planck Center for Visual Computing and Communication","oa_version":"Submitted Version","date_updated":"2023-10-18T08:06:45Z","date_created":"2018-12-11T11:55:12Z","author":[{"full_name":"Iglesias Ham, Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","last_name":"Iglesias Ham"},{"orcid":"0000-0002-8030-9299","last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"last_name":"Uhler","first_name":"Caroline","orcid":"0000-0002-7008-0216","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","full_name":"Uhler, Caroline"}],"type":"preprint","article_number":"1401.0468","publist_id":"5064","abstract":[{"text":"The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice.","lang":"eng"}]},{"scopus_import":1,"publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"month":"12","day":"01","page":"37 - 46","quality_controlled":"1","citation":{"ama":"Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11","apa":"Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia: IEEE. https://doi.org/10.1109/ISVD.2013.11","ieee":"T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.","ista":"Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.","short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.","mla":"Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11."},"language":[{"iso":"eng"}],"date_published":"2013-12-01T00:00:00Z","doi":"10.1109/ISVD.2013.11","conference":{"end_date":"2013-07-10","start_date":"2013-07-08","location":"St. Petersburg, Russia","name":"ISVD: Voronoi Diagrams in Science and Engineering"},"alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"type":"conference","publist_id":"4763","abstract":[{"lang":"eng","text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985.\r\n"}],"publisher":"IEEE","department":[{"_id":"HeEd"}],"publication_status":"published","status":"public","title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","_id":"2209","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","date_updated":"2021-01-12T06:56:00Z","date_created":"2018-12-11T11:56:20Z","author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"full_name":"Huber, Stefan","first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"}]},{"page":"95 - 98","main_file_link":[{"url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf","open_access":"1"}],"oa":1,"citation":{"ama":"Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: 29th European Workshop on Computational Geometry. TU Braunschweig; 2013:95-98.","ista":"Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight skeletons. 29th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 95–98.","apa":"Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In 29th European Workshop on Computational Geometry (pp. 95–98). Braunschweig, Germany: TU Braunschweig.","ieee":"T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig, Germany, 2013, pp. 95–98.","mla":"Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98.","short":"T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In 29th European Workshop on Computational Geometry, 95–98. TU Braunschweig, 2013."},"publication":"29th European Workshop on Computational Geometry","language":[{"iso":"eng"}],"date_published":"2013-03-01T00:00:00Z","conference":{"name":"EuroCG: European Workshop on Computational Geometry","start_date":"2013-03-17","location":"Braunschweig, Germany","end_date":"2013-03-20"},"day":"01","month":"03","publisher":"TU Braunschweig","department":[{"_id":"HeEd"}],"publication_status":"published","title":"Reconstructing polygons from embedded straight skeletons","status":"public","year":"2013","_id":"2210","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","date_updated":"2021-01-12T06:56:00Z","date_created":"2018-12-11T11:56:21Z","author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber"}],"type":"conference","publist_id":"4762","abstract":[{"text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon? We show that in most cases there exists at most one polygon; in the remaining case there is an infinite number of polygons determined by one angle that can range in an interval. We can find this (set of) polygon(s) in linear time in the Real RAM computer model.","lang":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1016/j.endm.2013.07.008","date_published":"2013-09-05T00:00:00Z","quality_controlled":"1","page":"43 - 50","publication":"Electronic Notes in Discrete Mathematics","citation":{"ista":"Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50.","ieee":"F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013.","apa":"Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008","ama":"Pausinger F. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008","chicago":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008.","mla":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008.","short":"F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50."},"day":"05","month":"09","scopus_import":1,"date_updated":"2021-01-12T06:56:39Z","date_created":"2018-12-11T11:56:53Z","oa_version":"None","volume":43,"author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger","full_name":"Pausinger, Florian"}],"publication_status":"published","status":"public","title":"Van der Corput sequences and linear permutations","intvolume":" 43","department":[{"_id":"HeEd"}],"publisher":"Elsevier","_id":"2304","acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013","abstract":[{"lang":"eng","text":"This extended abstract is concerned with the irregularities of distribution of one-dimensional permuted van der Corput sequences that are generated from linear permutations. We show how to obtain upper bounds for the discrepancy and diaphony of these sequences, by relating them to Kronecker sequences and applying earlier results of Faure and Niederreiter."}],"publist_id":"4623","type":"journal_article"},{"file_date_updated":"2020-07-14T12:45:48Z","publist_id":"4078","publication_status":"published","publisher":"ACM","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"year":"2013","date_updated":"2021-01-12T06:59:51Z","date_created":"2018-12-11T11:59:42Z","author":[{"full_name":"Čadek, Martin","last_name":"Čadek","first_name":"Martin"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"last_name":"Vokřínek","first_name":"Lukáš","full_name":"Vokřínek, Lukáš"},{"first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli"}],"month":"06","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"conference":{"name":"STOC: Symposium on the Theory of Computing","start_date":"2013-06-01","location":"Palo Alto, CA, United States","end_date":"2013-06-04"},"doi":"10.1145/2488608.2488683","type":"conference","abstract":[{"text":"We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces X; Y , a subspace A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X → Y . For computational purposes, we assume that X and Y are represented as finite simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov's result from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected; informally, this means that Y has \\no holes up to dimension k-1" (a basic example of such a Y is the sphere Sk). We prove that, on the one hand, this problem is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2, we obtain an algorithm that solves the extension problem in polynomial time assuming Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected Y . Their computability was established by Brown in 1957; we show that πk(Y ) can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where Y is a cell complex with certain rather compact encoding. We strengthen his result to #P-hardness for Y given as a simplicial complex. ","lang":"eng"}],"ddc":["510"],"status":"public","title":"Extending continuous maps: Polynomiality and undecidability","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2807","file":[{"content_type":"application/pdf","file_size":447945,"creator":"system","file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","access_level":"open_access","date_created":"2018-12-12T10:14:29Z","date_updated":"2020-07-14T12:45:48Z","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","relation":"main_file","file_id":"5081"}],"oa_version":"Submitted Version","pubrep_id":"533","scopus_import":1,"day":"01","has_accepted_license":"1","page":"595 - 604","publication":"45th Annual ACM Symposium on theory of computing","citation":{"ista":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of computing. STOC: Symposium on the Theory of Computing, 595–604.","apa":"Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013). Extending continuous maps: Polynomiality and undecidability. In 45th Annual ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United States: ACM. https://doi.org/10.1145/2488608.2488683","ieee":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory of computing, Palo Alto, CA, United States, 2013, pp. 595–604.","ama":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps: Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner. “Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.","mla":"Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.” 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604, doi:10.1145/2488608.2488683.","short":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604."},"date_published":"2013-06-01T00:00:00Z"}]