[{"conference":{"start_date":"2014-06-08","location":"Kyoto, Japan","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry"},"ec_funded":1,"publication":"Proceedings of the Annual Symposium on Computational Geometry","acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","status":"public","main_file_link":[{"url":"http://arxiv.org/abs/1307.2839","open_access":"1"}],"date_created":"2018-12-11T11:56:02Z","article_processing_charge":"No","author":[{"last_name":"Bauer","full_name":"Bauer, Ulrich","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"full_name":"Ge, Xiaoyin","last_name":"Ge","first_name":"Xiaoyin"},{"first_name":"Yusu","full_name":"Wang, Yusu","last_name":"Wang"}],"abstract":[{"text":"We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).","lang":"eng"}],"date_updated":"2025-06-11T07:58:42Z","oa_version":"Submitted Version","day":"01","title":"Measuring distance between Reeb graphs","project":[{"grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems"}],"department":[{"_id":"HeEd"}],"page":"464 - 473","external_id":{"arxiv":["1307.2839"]},"year":"2014","quality_controlled":"1","date_published":"2014-06-01T00:00:00Z","doi":"10.1145/2582112.2582169","publisher":"ACM","language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","citation":{"short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.","chicago":"Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 464–73. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582169\">https://doi.org/10.1145/2582112.2582169</a>.","mla":"Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 464–73, doi:<a href=\"https://doi.org/10.1145/2582112.2582169\">10.1145/2582112.2582169</a>.","ista":"Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.","ama":"Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:464-473. doi:<a href=\"https://doi.org/10.1145/2582112.2582169\">10.1145/2582112.2582169</a>","apa":"Bauer, U., Ge, X., &#38; Wang, Y. (2014). Measuring distance between Reeb graphs. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 464–473). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582169\">https://doi.org/10.1145/2582112.2582169</a>","ieee":"U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 464–473."},"publication_status":"published","scopus_import":"1","month":"06","publist_id":"4850","arxiv":1,"_id":"2156"},{"type":"conference","abstract":[{"text":"We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity.","lang":"eng"}],"corr_author":"1","date_updated":"2024-10-09T20:55:33Z","citation":{"ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Portland, USA, 2014, pp. 152–160.","ama":"Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>. SIAM; 2014:152-160. doi:<a href=\"https://doi.org/10.1137/1.9781611973402.11\">10.1137/1.9781611973402.11</a>","apa":"Edelsbrunner, H., &#38; Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 152–160). Portland, USA: SIAM. <a href=\"https://doi.org/10.1137/1.9781611973402.11\">https://doi.org/10.1137/1.9781611973402.11</a>","chicago":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 152–60. SIAM, 2014. <a href=\"https://doi.org/10.1137/1.9781611973402.11\">https://doi.org/10.1137/1.9781611973402.11</a>.","ista":"Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.","mla":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, SIAM, 2014, pp. 152–60, doi:<a href=\"https://doi.org/10.1137/1.9781611973402.11\">10.1137/1.9781611973402.11</a>.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160."},"oa_version":"None","publication_status":"published","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","first_name":"Salman","full_name":"Parsa, Salman","last_name":"Parsa"}],"department":[{"_id":"HeEd"}],"_id":"2177","month":"01","day":"01","scopus_import":1,"publist_id":"4805","title":"On the computational complexity of betti numbers reductions from matrix rank","publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","year":"2014","quality_controlled":"1","page":"152 - 160","conference":{"name":"SODA: Symposium on Discrete Algorithms","end_date":"2014-01-07","location":"Portland, USA","start_date":"2014-01-05"},"language":[{"iso":"eng"}],"doi":"10.1137/1.9781611973402.11","date_published":"2014-01-01T00:00:00Z","publisher":"SIAM","status":"public","date_created":"2018-12-11T11:56:09Z"},{"status":"public","date_created":"2018-12-11T11:56:12Z","main_file_link":[{"url":"http://arxiv.org/abs/1105.6257","open_access":"1"}],"acknowledgement":"The research by M. K. was supported by project GAUK 49209. The research by M. K. was also supported by project 1M0545 by the Ministry of Education of the Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague (project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).","article_processing_charge":"No","publication":"Journal of the ACM","title":"Computing all maps into a sphere","day":"01","isi":1,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"author":[{"first_name":"Martin","full_name":"Čadek, Martin","last_name":"Čadek"},{"first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","full_name":"Krcál, Marek"},{"first_name":"Jiří","full_name":"Matoušek, Jiří","last_name":"Matoušek"},{"last_name":"Sergeraert","full_name":"Sergeraert, Francis","first_name":"Francis"},{"first_name":"Lukáš","full_name":"Vokřínek, Lukáš","last_name":"Vokřínek"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","full_name":"Wagner, Uli","last_name":"Wagner"}],"date_updated":"2025-09-29T11:34:15Z","intvolume":"        61","oa_version":"Preprint","article_number":"17 ","abstract":[{"lang":"eng","text":"Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable."}],"oa":1,"issue":"3","language":[{"iso":"eng"}],"doi":"10.1145/2597629","date_published":"2014-05-01T00:00:00Z","publisher":"ACM","external_id":{"isi":["000337201400003"],"arxiv":["1105.6257"]},"year":"2014","quality_controlled":"1","publist_id":"4797","arxiv":1,"scopus_import":"1","month":"05","_id":"2184","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"apa":"Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., &#38; Wagner, U. (2014). Computing all maps into a sphere. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2597629\">https://doi.org/10.1145/2597629</a>","ama":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. <i>Journal of the ACM</i>. 2014;61(3). doi:<a href=\"https://doi.org/10.1145/2597629\">10.1145/2597629</a>","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” <i>Journal of the ACM</i>, vol. 61, no. 3. ACM, 2014.","mla":"Čadek, Martin, et al. “Computing All Maps into a Sphere.” <i>Journal of the ACM</i>, vol. 61, no. 3, 17, ACM, 2014, doi:<a href=\"https://doi.org/10.1145/2597629\">10.1145/2597629</a>.","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere.” <i>Journal of the ACM</i>. ACM, 2014. <a href=\"https://doi.org/10.1145/2597629\">https://doi.org/10.1145/2597629</a>.","ista":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing all maps into a sphere. Journal of the ACM. 61(3), 17.","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014)."},"publication_status":"published","type":"journal_article","volume":61},{"publication":"Moscow Mathematical Journal","publication_identifier":{"issn":["1609-3321"]},"article_processing_charge":"No","status":"public","date_created":"2018-12-11T11:54:29Z","main_file_link":[{"url":"http://arxiv.org/abs/1211.7053","open_access":"1"}],"abstract":[{"lang":"eng","text":"We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets."}],"date_updated":"2025-07-10T11:51:26Z","intvolume":"        14","oa_version":"Submitted Version","author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"first_name":"Oleg","last_name":"Musin","full_name":"Musin, Oleg"}],"department":[{"_id":"HeEd"}],"day":"01","title":"Functionals on triangulations of delaunay sets","year":"2014","quality_controlled":"1","page":"491 - 504","external_id":{"arxiv":["1211.7053"]},"article_type":"original","issue":"3","language":[{"iso":"eng"}],"doi":"10.17323/1609-4514-2014-14-3-491-504","publisher":"Independent University of Moscow","date_published":"2014-07-01T00:00:00Z","oa":1,"type":"journal_article","volume":14,"citation":{"ieee":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations of delaunay sets,” <i>Moscow Mathematical Journal</i>, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014.","apa":"Dolbilin, N., Edelsbrunner, H., Glazyrin, A., &#38; Musin, O. (2014). Functionals on triangulations of delaunay sets. <i>Moscow Mathematical Journal</i>. Independent University of Moscow. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">https://doi.org/10.17323/1609-4514-2014-14-3-491-504</a>","ama":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations of delaunay sets. <i>Moscow Mathematical Journal</i>. 2014;14(3):491-504. doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">10.17323/1609-4514-2014-14-3-491-504</a>","mla":"Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” <i>Moscow Mathematical Journal</i>, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">10.17323/1609-4514-2014-14-3-491-504</a>.","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” <i>Moscow Mathematical Journal</i>. Independent University of Moscow, 2014. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">https://doi.org/10.17323/1609-4514-2014-14-3-491-504</a>.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504."},"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1876","month":"07","scopus_import":"1","publist_id":"5220","arxiv":1},{"publication":"Journal of Mathematical Sciences","publication_identifier":{"eissn":["1573-8795"],"issn":["1072-3374"]},"article_processing_charge":"No","date_created":"2018-12-11T11:54:46Z","status":"public","acknowledgement":"We would like to offer our special thanks to students of the Department of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev for participation in developing the program and assistance in preparation of test data. This work was supported by grant 11.G34.31.0053 from the government of the Russian Federation.","oa_version":"None","date_updated":"2022-05-24T10:39:06Z","intvolume":"       203","abstract":[{"text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales.","lang":"eng"}],"author":[{"first_name":"V V","full_name":"Alexeev, V V","last_name":"Alexeev"},{"first_name":"V G","last_name":"Bogaevskaya","full_name":"Bogaevskaya, V G"},{"full_name":"Preobrazhenskaya, M M","last_name":"Preobrazhenskaya","first_name":"M M"},{"last_name":"Ukhalov","full_name":"Ukhalov, A Y","first_name":"A Y"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Yakimova","full_name":"Yakimova, Olga","first_name":"Olga"}],"department":[{"_id":"HeEd"}],"title":"An algorithm for cartographic generalization that preserves global topology","day":"16","quality_controlled":"1","year":"2014","page":"754 - 760","article_type":"original","publisher":"Springer","date_published":"2014-11-16T00:00:00Z","doi":"10.1007/s10958-014-2165-8","language":[{"iso":"eng"}],"issue":"6","publication_status":"published","citation":{"short":"V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner, O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.","mla":"Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” <i>Journal of Mathematical Sciences</i>, vol. 203, no. 6, Springer, 2014, pp. 754–60, doi:<a href=\"https://doi.org/10.1007/s10958-014-2165-8\">10.1007/s10958-014-2165-8</a>.","chicago":"Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” <i>Journal of Mathematical Sciences</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s10958-014-2165-8\">https://doi.org/10.1007/s10958-014-2165-8</a>.","ista":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 203(6), 754–760.","apa":"Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., &#38; Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. <i>Journal of Mathematical Sciences</i>. Springer. <a href=\"https://doi.org/10.1007/s10958-014-2165-8\">https://doi.org/10.1007/s10958-014-2165-8</a>","ama":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. An algorithm for cartographic generalization that preserves global topology. <i>Journal of Mathematical Sciences</i>. 2014;203(6):754-760. doi:<a href=\"https://doi.org/10.1007/s10958-014-2165-8\">10.1007/s10958-014-2165-8</a>","ieee":"V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” <i>Journal of Mathematical Sciences</i>, vol. 203, no. 6. Springer, pp. 754–760, 2014."},"type":"journal_article","volume":203,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1929","publist_id":"5165","month":"11","scopus_import":"1"},{"type":"journal_article","volume":20,"citation":{"short":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T. Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.","mla":"Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:<a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">10.1109/TVCG.2014.2346432</a>.","chicago":"Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” <i>IEEE Transactions on Visualization and Computer Graphics</i>. IEEE, 2014. <a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">https://doi.org/10.1109/TVCG.2014.2346432</a>.","ista":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.","ieee":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar fields,” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 20, no. 12. IEEE, pp. 2585–2594, 2014.","apa":"Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O., &#38; Weinkauf, T. (2014). Fast and memory-efficient topological denoising of 2D and 3D scalar fields. <i>IEEE Transactions on Visualization and Computer Graphics</i>. IEEE. <a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">https://doi.org/10.1109/TVCG.2014.2346432</a>","ama":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. <i>IEEE Transactions on Visualization and Computer Graphics</i>. 2014;20(12):2585-2594. doi:<a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">10.1109/TVCG.2014.2346432</a>"},"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"1930","scopus_import":"1","month":"12","publist_id":"5164","year":"2014","quality_controlled":"1","page":"2585 - 2594","external_id":{"isi":["000344991700104"]},"issue":"12","date_published":"2014-12-31T00:00:00Z","doi":"10.1109/TVCG.2014.2346432","language":[{"iso":"eng"}],"publisher":"IEEE","abstract":[{"text":"(Figure Presented) Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications.","lang":"eng"}],"date_updated":"2025-09-29T12:11:45Z","intvolume":"        20","oa_version":"None","author":[{"first_name":"David","full_name":"Günther, David","last_name":"Günther"},{"first_name":"Alec","full_name":"Jacobson, Alec","last_name":"Jacobson"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus"},{"full_name":"Seidel, Hans","last_name":"Seidel","first_name":"Hans"},{"full_name":"Sorkine Hornung, Olga","last_name":"Sorkine Hornung","first_name":"Olga"},{"first_name":"Tino","last_name":"Weinkauf","full_name":"Weinkauf, Tino"}],"department":[{"_id":"HeEd"}],"isi":1,"day":"31","title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","publication":"IEEE Transactions on Visualization and Computer Graphics","article_processing_charge":"No","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","status":"public","date_created":"2018-12-11T11:54:46Z"},{"publication_status":"published","citation":{"mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” <i>26th Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2014, pp. 155–61.","chicago":"Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” In <i>26th Canadian Conference on Computational Geometry</i>, 155–61. Canadian Conference on Computational Geometry, 2014.","ista":"Iglesias Ham M, Kerber M, Uhler C. 2014. Sphere packing with limited overlap. 26th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry, 155–161.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, in:, 26th Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2014, pp. 155–161.","ieee":"M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” in <i>26th Canadian Conference on Computational Geometry</i>, Halifax, Canada, 2014, pp. 155–161.","apa":"Iglesias Ham, M., Kerber, M., &#38; Uhler, C. (2014). Sphere packing with limited overlap. In <i>26th Canadian Conference on Computational Geometry</i> (pp. 155–161). Halifax, Canada: Canadian Conference on Computational Geometry.","ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. In: <i>26th Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2014:155-161."},"type":"conference","corr_author":"1","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2012","arxiv":1,"publist_id":"5064","scopus_import":"1","month":"09","quality_controlled":"1","year":"2014","external_id":{"arxiv":["1401.0468"]},"page":"155-161","oa":1,"date_published":"2014-09-01T00:00:00Z","language":[{"iso":"eng"}],"publisher":"Canadian Conference on Computational Geometry","oa_version":"Preprint","date_updated":"2025-01-20T13:57:24Z","abstract":[{"lang":"eng","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."}],"author":[{"first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel"},{"first_name":"Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","full_name":"Kerber, Michael"},{"orcid":"0000-0002-7008-0216","first_name":"Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","full_name":"Uhler, Caroline","last_name":"Uhler"}],"OA_type":"green","department":[{"_id":"HeEd"},{"_id":"CaUh"}],"title":"Sphere packing with limited overlap","day":"01","publication":"26th Canadian Conference on Computational Geometry","conference":{"location":"Halifax, Canada","start_date":"2014-08-11","end_date":"2014-08-13","name":"CCCG: Canadian Conference on Computational Geometry"},"article_processing_charge":"No","main_file_link":[{"url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf","open_access":"1"}],"date_created":"2018-12-11T11:55:12Z","status":"public","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"},{"type":"conference","citation":{"apa":"Bauer, U., Kerber, M., &#38; Reininghaus, J. (2014). Distributed computation of persistent homology. In C.  McGeoch &#38; U. Meyer (Eds.), <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i> (pp. 31–38). Portland, USA: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611973198.4\">https://doi.org/10.1137/1.9781611973198.4</a>","ama":"Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology. In:  McGeoch C, Meyer U, eds. <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>. Society for Industrial and Applied Mathematics; 2014:31-38. doi:<a href=\"https://doi.org/10.1137/1.9781611973198.4\">10.1137/1.9781611973198.4</a>","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” in <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>, Portland, USA, 2014, pp. 31–38.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, C.  McGeoch, U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics, 2014, pp. 31–38.","ista":"Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent homology. Proceedings of the Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, 31–38.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation of Persistent Homology.” In <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>, edited by Catherine  McGeoch and Ulrich Meyer, 31–38. Society for Industrial and Applied Mathematics, 2014. <a href=\"https://doi.org/10.1137/1.9781611973198.4\">https://doi.org/10.1137/1.9781611973198.4</a>.","mla":"Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>, edited by Catherine  McGeoch and Ulrich Meyer, Society for Industrial and Applied Mathematics, 2014, pp. 31–38, doi:<a href=\"https://doi.org/10.1137/1.9781611973198.4\">10.1137/1.9781611973198.4</a>."},"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","editor":[{"full_name":" McGeoch, Catherine","last_name":" McGeoch","first_name":"Catherine"},{"first_name":"Ulrich","last_name":"Meyer","full_name":"Meyer, Ulrich"}],"_id":"2043","scopus_import":"1","month":"01","publist_id":"5008","arxiv":1,"year":"2014","quality_controlled":"1","page":"31 - 38","external_id":{"arxiv":["1310.0710"]},"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","publisher":"Society for Industrial and Applied Mathematics","doi":"10.1137/1.9781611973198.4","oa":1,"abstract":[{"lang":"eng","text":"Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems [1], we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 6GB of memory per node."}],"date_updated":"2025-06-11T08:03:07Z","oa_version":"Submitted Version","author":[{"full_name":"Bauer, Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"orcid":"0000-0002-8030-9299","first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"}],"project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7"}],"department":[{"_id":"HeEd"}],"day":"01","title":"Distributed computation of persistent homology","publication":"Proceedings of the Workshop on Algorithm Engineering and Experiments","conference":{"location":"Portland, USA","start_date":"2014-01-05","end_date":"2014-01-05","name":"ALENEX: Algorithm Engineering and Experiments"},"ec_funded":1,"article_processing_charge":"No","status":"public","date_created":"2018-12-11T11:55:23Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.0710"}]},{"department":[{"_id":"HeEd"}],"project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7"}],"title":"Clear and Compress: Computing Persistent Homology in Chunks","day":"19","oa_version":"Submitted Version","date_updated":"2025-06-11T07:56:57Z","abstract":[{"text":"We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.","lang":"eng"}],"author":[{"last_name":"Bauer","full_name":"Bauer, Ulrich","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"full_name":"Kerber, Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299","first_name":"Michael"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","date_created":"2018-12-11T11:55:23Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1303.0477"}],"status":"public","publication":"Topological Methods in Data Analysis and Visualization III","ec_funded":1,"_id":"2044","arxiv":1,"publist_id":"5007","month":"03","scopus_import":"1","publication_status":"published","citation":{"ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in <i>Topological Methods in Data Analysis and Visualization III</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.","apa":"Bauer, U., Kerber, M., &#38; Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III</i> (pp. 103–117). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">https://doi.org/10.1007/978-3-319-04099-8_7</a>","ama":"Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III</i>. Mathematics and Visualization. Springer; 2014:103-117. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">10.1007/978-3-319-04099-8_7</a>","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In <i>Topological Methods in Data Analysis and Visualization III</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">https://doi.org/10.1007/978-3-319-04099-8_7</a>.","mla":"Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” <i>Topological Methods in Data Analysis and Visualization III</i>, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">10.1007/978-3-319-04099-8_7</a>.","ista":"Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117."},"type":"book_chapter","corr_author":"1","series_title":"Mathematics and Visualization","editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"first_name":"Valerio","full_name":"Pascucci, Valerio","last_name":"Pascucci"},{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Springer","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_7","date_published":"2014-03-19T00:00:00Z","quality_controlled":"1","year":"2014","external_id":{"arxiv":["1303.0477"]},"page":"103 - 117"},{"publication":"International Journal of Computational Geometry and Applications","pubrep_id":"443","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","date_created":"2018-12-11T11:54:10Z","file_date_updated":"2020-07-14T12:45:17Z","status":"public","abstract":[{"lang":"eng","text":"Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques."}],"oa_version":"Published Version","intvolume":"        24","date_updated":"2024-10-09T20:55:54Z","author":[{"full_name":"Huber, Stefan","last_name":"Huber","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"first_name":"Peter","last_name":"Meerwald","full_name":"Meerwald, Peter"},{"first_name":"Roland","last_name":"Kwitt","full_name":"Kwitt, Roland"}],"department":[{"_id":"HeEd"}],"has_accepted_license":"1","ddc":["000"],"day":"16","title":"Topology-preserving watermarking of vector graphics","quality_controlled":"1","year":"2014","page":"61 - 86","doi":"10.1142/S0218195914500034","publisher":"World Scientific Publishing","language":[{"iso":"eng"}],"date_published":"2014-03-16T00:00:00Z","issue":"1","file":[{"creator":"system","relation":"main_file","date_created":"2018-12-12T10:08:43Z","file_size":991734,"date_updated":"2020-07-14T12:45:17Z","content_type":"application/pdf","checksum":"be45c133ab4d43351260e21beaa8f4b1","access_level":"open_access","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","file_id":"4704"}],"oa":1,"type":"journal_article","corr_author":"1","volume":24,"publication_status":"published","citation":{"ama":"Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. <i>International Journal of Computational Geometry and Applications</i>. 2014;24(1):61-86. doi:<a href=\"https://doi.org/10.1142/S0218195914500034\">10.1142/S0218195914500034</a>","apa":"Huber, S., Held, M., Meerwald, P., &#38; Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. <i>International Journal of Computational Geometry and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218195914500034\">https://doi.org/10.1142/S0218195914500034</a>","ieee":"S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” <i>International Journal of Computational Geometry and Applications</i>, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86.","ista":"Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 24(1), 61–86.","mla":"Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” <i>International Journal of Computational Geometry and Applications</i>, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:<a href=\"https://doi.org/10.1142/S0218195914500034\">10.1142/S0218195914500034</a>.","chicago":"Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving Watermarking of Vector Graphics.” <i>International Journal of Computational Geometry and Applications</i>. World Scientific Publishing, 2014. <a href=\"https://doi.org/10.1142/S0218195914500034\">https://doi.org/10.1142/S0218195914500034</a>."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"_id":"1816","scopus_import":1,"month":"03","publist_id":"5290"},{"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7004"}],"date_created":"2018-12-11T11:54:18Z","status":"public","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","article_processing_charge":"No","publication":"Discrete & Computational Geometry","title":"On the geometric ramsey number of outerplanar graphs","day":"14","isi":1,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"author":[{"full_name":"Cibulka, Josef","last_name":"Cibulka","first_name":"Josef"},{"full_name":"Gao, Pu","last_name":"Gao","first_name":"Pu"},{"first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","full_name":"Krcál, Marek"},{"last_name":"Valla","full_name":"Valla, Tomáš","first_name":"Tomáš"},{"last_name":"Valtr","full_name":"Valtr, Pavel","first_name":"Pavel"}],"oa_version":"Submitted Version","intvolume":"        53","date_updated":"2025-09-29T13:11:56Z","abstract":[{"text":"We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices.","lang":"eng"}],"oa":1,"doi":"10.1007/s00454-014-9646-x","language":[{"iso":"eng"}],"publisher":"Springer","date_published":"2014-11-14T00:00:00Z","issue":"1","external_id":{"arxiv":["1310.7004"],"isi":["000346774600005"]},"page":"64 - 79","year":"2014","arxiv":1,"publist_id":"5260","month":"11","scopus_import":"1","_id":"1842","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","citation":{"ista":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete &#38; Computational Geometry. 53(1), 64–79.","mla":"Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” <i>Discrete &#38; Computational Geometry</i>, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:<a href=\"https://doi.org/10.1007/s00454-014-9646-x\">10.1007/s00454-014-9646-x</a>.","chicago":"Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00454-014-9646-x\">https://doi.org/10.1007/s00454-014-9646-x</a>.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete &#38; Computational Geometry 53 (2014) 64–79.","ieee":"J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” <i>Discrete &#38; Computational Geometry</i>, vol. 53, no. 1. Springer, pp. 64–79, 2014.","apa":"Cibulka, J., Gao, P., Krcál, M., Valla, T., &#38; Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-014-9646-x\">https://doi.org/10.1007/s00454-014-9646-x</a>","ama":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. <i>Discrete &#38; Computational Geometry</i>. 2014;53(1):64-79. doi:<a href=\"https://doi.org/10.1007/s00454-014-9646-x\">10.1007/s00454-014-9646-x</a>"},"type":"journal_article","volume":53},{"department":[{"_id":"HeEd"}],"_id":"6853","scopus_import":"1","day":"01","alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"month":"01","place":"Cham","title":"A Short Course in Computational Geometry and Topology","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."}],"type":"book","edition":"1","date_updated":"2022-03-04T07:47:54Z","citation":{"chicago":"Edelsbrunner, Herbert. <i>A Short Course in Computational Geometry and Topology</i>. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham: Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-05957-0\">https://doi.org/10.1007/978-3-319-05957-0</a>.","ista":"Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.","mla":"Edelsbrunner, Herbert. <i>A Short Course in Computational Geometry and Topology</i>. 1st ed., Springer Nature, 2014, doi:<a href=\"https://doi.org/10.1007/978-3-319-05957-0\">10.1007/978-3-319-05957-0</a>.","short":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014.","ama":"Edelsbrunner H. <i>A Short Course in Computational Geometry and Topology</i>. 1st ed. Cham: Springer Nature; 2014. doi:<a href=\"https://doi.org/10.1007/978-3-319-05957-0\">10.1007/978-3-319-05957-0</a>","apa":"Edelsbrunner, H. (2014). <i>A Short Course in Computational Geometry and Topology</i> (1st ed.). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-05957-0\">https://doi.org/10.1007/978-3-319-05957-0</a>","ieee":"H. Edelsbrunner, <i>A Short Course in Computational Geometry and Topology</i>, 1st ed. Cham: Springer Nature, 2014."},"publication_status":"published","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"series_title":"SpringerBriefs in Applied Sciences and Technology","article_processing_charge":"No","publisher":"Springer Nature","date_published":"2014-01-01T00:00:00Z","doi":"10.1007/978-3-319-05957-0","language":[{"iso":"eng"}],"status":"public","date_created":"2019-09-06T09:22:33Z","related_material":{"link":[{"description":"available as eBook via catalog IST BookList","relation":"other","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106"},{"url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842","description":"available via catalog IST BookList","relation":"other"}]},"year":"2014","quality_controlled":"1","publication_identifier":{"eisbn":["9-783-3190-5957-0"],"issn":["2191-530X"],"isbn":["9-783-3190-5956-3"],"eissn":["2191-5318"]},"page":"IX, 110"},{"year":"2013","quality_controlled":"1","page":"182-183","publisher":"Springer Nature","doi":"10.1007/978-3-642-38221-5_19","date_published":"2013-06-01T00:00:00Z","language":[{"iso":"eng"}],"citation":{"short":"H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition, Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183.","mla":"Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” <i>Graph-Based Representations in Pattern Recognition</i>, vol. 7877, Springer Nature, 2013, pp. 182–83, doi:<a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">10.1007/978-3-642-38221-5_19</a>.","ista":"Edelsbrunner H. 2013. Persistent homology in image processing. Graph-Based Representations in Pattern Recognition. GbRPR: Graph-based Representations in Pattern RecognitionLNCS vol. 7877, 182–183.","chicago":"Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In <i>Graph-Based Representations in Pattern Recognition</i>, 7877:182–83. LNCS. Berlin, Heidelberg: Springer Nature, 2013. <a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">https://doi.org/10.1007/978-3-642-38221-5_19</a>.","apa":"Edelsbrunner, H. (2013). Persistent homology in image processing. In <i>Graph-Based Representations in Pattern Recognition</i> (Vol. 7877, pp. 182–183). Berlin, Heidelberg: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">https://doi.org/10.1007/978-3-642-38221-5_19</a>","ama":"Edelsbrunner H. Persistent homology in image processing. In: <i>Graph-Based Representations in Pattern Recognition</i>. Vol 7877. LNCS. Berlin, Heidelberg: Springer Nature; 2013:182-183. doi:<a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">10.1007/978-3-642-38221-5_19</a>","ieee":"H. Edelsbrunner, “Persistent homology in image processing,” in <i>Graph-Based Representations in Pattern Recognition</i>, Vienna, Austria, 2013, vol. 7877, pp. 182–183."},"publication_status":"published","corr_author":"1","type":"conference","volume":7877,"series_title":"LNCS","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10897","month":"06","scopus_import":"1","publication":"Graph-Based Representations in Pattern Recognition","conference":{"location":"Vienna, Austria","start_date":"2013-05-15","end_date":"2013-05-17","name":"GbRPR: Graph-based Representations in Pattern Recognition"},"ec_funded":1,"publication_identifier":{"eisbn":["9783642382215"],"issn":["0302-9743"],"isbn":["9783642382208"],"eissn":["1611-3349"]},"article_processing_charge":"No","status":"public","date_created":"2022-03-21T07:30:33Z","acknowledgement":"This research is partially supported by the European Science Foundation (ESF) under the Research Network Programme, the European Union under the Toposys Project FP7-ICT-318493-STREP, the Russian Government under the Mega Project 11.G34.31.0053.","intvolume":"      7877","date_updated":"2025-04-15T08:37:54Z","oa_version":"None","abstract":[{"text":"Taking images is an efficient way to collect data about the physical world. It can be done fast and in exquisite detail. By definition, image processing is the field that concerns itself with the computation aimed at harnessing the information contained in images [10]. This talk is concerned with topological information. Our main thesis is that persistent homology [5] is a useful method to quantify and summarize topological information, building a bridge that connects algebraic topology with applications. We provide supporting evidence for this thesis by touching upon four technical developments in the overlap between persistent homology and image processing.","lang":"eng"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"HeEd"}],"place":"Berlin, Heidelberg","title":"Persistent homology in image processing","day":"01"},{"department":[{"_id":"HeEd"}],"_id":"2209","isi":1,"month":"12","day":"01","alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"scopus_import":"1","publist_id":"4763","title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","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"}],"type":"conference","date_updated":"2025-09-29T14:30:56Z","citation":{"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.","mla":"Biedl, Therese, et al. <i>Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input</i>. IEEE, 2013, pp. 37–46, doi:<a href=\"https://doi.org/10.1109/ISVD.2013.11\">10.1109/ISVD.2013.11</a>.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. <a href=\"https://doi.org/10.1109/ISVD.2013.11\">https://doi.org/10.1109/ISVD.2013.11</a>.","short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.","apa":"Biedl, T., Held, M., &#38; 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. <a href=\"https://doi.org/10.1109/ISVD.2013.11\">https://doi.org/10.1109/ISVD.2013.11</a>","ama":"Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:<a href=\"https://doi.org/10.1109/ISVD.2013.11\">10.1109/ISVD.2013.11</a>","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."},"oa_version":"None","publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"last_name":"Huber","full_name":"Huber, Stefan","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"}],"article_processing_charge":"No","doi":"10.1109/ISVD.2013.11","date_published":"2013-12-01T00:00:00Z","publisher":"IEEE","language":[{"iso":"eng"}],"status":"public","date_created":"2018-12-11T11:56:20Z","year":"2013","quality_controlled":"1","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"page":"37 - 46","conference":{"end_date":"2013-07-10","name":"ISVD: Voronoi Diagrams in Science and Engineering","location":"St. Petersburg, Russia","start_date":"2013-07-08"},"external_id":{"isi":["000430602800007"]}},{"department":[{"_id":"HeEd"}],"_id":"2210","day":"01","month":"03","title":"Reconstructing polygons from embedded straight skeletons","publist_id":"4762","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. 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."}],"type":"conference","publication_status":"published","oa_version":"Submitted Version","citation":{"chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In <i>29th European Workshop on Computational Geometry</i>, 95–98. TU Braunschweig, 2013.","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.","mla":"Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” <i>29th European Workshop on Computational Geometry</i>, 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.","apa":"Biedl, T., Held, M., &#38; Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In <i>29th European Workshop on Computational Geometry</i> (pp. 95–98). Braunschweig, Germany: TU Braunschweig.","ama":"Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: <i>29th European Workshop on Computational Geometry</i>. TU Braunschweig; 2013:95-98.","ieee":"T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in <i>29th European Workshop on Computational Geometry</i>, Braunschweig, Germany, 2013, pp. 95–98."},"date_updated":"2021-01-12T06:56:00Z","author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","full_name":"Huber, Stefan"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publisher":"TU Braunschweig","date_published":"2013-03-01T00:00:00Z","date_created":"2018-12-11T11:56:21Z","main_file_link":[{"url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf","open_access":"1"}],"status":"public","oa":1,"publication":"29th European Workshop on Computational Geometry","year":"2013","page":"95 - 98","conference":{"name":"EuroCG: European Workshop on Computational Geometry","end_date":"2013-03-20","location":"Braunschweig, Germany","start_date":"2013-03-17"}},{"publication":"Electronic Notes in Discrete Mathematics","year":"2013","quality_controlled":"1","page":"43 - 50","acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","language":[{"iso":"eng"}],"date_published":"2013-09-05T00:00:00Z","doi":"10.1016/j.endm.2013.07.008","publisher":"Elsevier","status":"public","date_created":"2018-12-11T11:56:53Z","type":"journal_article","abstract":[{"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.","lang":"eng"}],"volume":43,"corr_author":"1","citation":{"ieee":"F. Pausinger, “Van der Corput sequences and linear permutations,” <i>Electronic Notes in Discrete Mathematics</i>, vol. 43. Elsevier, pp. 43–50, 2013.","ama":"Pausinger F. Van der Corput sequences and linear permutations. <i>Electronic Notes in Discrete Mathematics</i>. 2013;43:43-50. doi:<a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">10.1016/j.endm.2013.07.008</a>","apa":"Pausinger, F. (2013). Van der Corput sequences and linear permutations. <i>Electronic Notes in Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">https://doi.org/10.1016/j.endm.2013.07.008</a>","short":"F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.","ista":"Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50.","chicago":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2013. <a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">https://doi.org/10.1016/j.endm.2013.07.008</a>.","mla":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” <i>Electronic Notes in Discrete Mathematics</i>, vol. 43, Elsevier, 2013, pp. 43–50, doi:<a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">10.1016/j.endm.2013.07.008</a>."},"intvolume":"        43","date_updated":"2024-10-09T20:55:15Z","publication_status":"published","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Pausinger, Florian","last_name":"Pausinger","orcid":"0000-0002-8379-3768","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"HeEd"}],"_id":"2304","day":"05","month":"09","scopus_import":1,"publist_id":"4623","title":"Van der Corput sequences and linear permutations"},{"page":"595 - 604","year":"2013","quality_controlled":"1","publisher":"ACM","date_published":"2013-06-01T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1145/2488608.2488683","oa":1,"file":[{"file_size":447945,"date_updated":"2020-07-14T12:45:48Z","content_type":"application/pdf","access_level":"open_access","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","file_id":"5081","creator":"system","relation":"main_file","date_created":"2018-12-12T10:14:29Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","citation":{"chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner. “Extending Continuous Maps: Polynomiality and Undecidability.” In <i>45th Annual ACM Symposium on Theory of Computing</i>, 595–604. ACM, 2013. <a href=\"https://doi.org/10.1145/2488608.2488683\">https://doi.org/10.1145/2488608.2488683</a>.","mla":"Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.” <i>45th Annual ACM Symposium on Theory of Computing</i>, ACM, 2013, pp. 595–604, doi:<a href=\"https://doi.org/10.1145/2488608.2488683\">10.1145/2488608.2488683</a>.","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.","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.","apa":"Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., &#38; Wagner, U. (2013). Extending continuous maps: Polynomiality and undecidability. In <i>45th Annual ACM Symposium on theory of computing</i> (pp. 595–604). Palo Alto, CA, United States: ACM. <a href=\"https://doi.org/10.1145/2488608.2488683\">https://doi.org/10.1145/2488608.2488683</a>","ama":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps: Polynomiality and undecidability. In: <i>45th Annual ACM Symposium on Theory of Computing</i>. ACM; 2013:595-604. doi:<a href=\"https://doi.org/10.1145/2488608.2488683\">10.1145/2488608.2488683</a>","ieee":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous maps: Polynomiality and undecidability,” in <i>45th Annual ACM Symposium on theory of computing</i>, Palo Alto, CA, United States, 2013, pp. 595–604."},"publication_status":"published","scopus_import":1,"month":"06","publist_id":"4078","_id":"2807","pubrep_id":"533","conference":{"name":"STOC: Symposium on the Theory of Computing","end_date":"2013-06-04","location":"Palo Alto, CA, United States","start_date":"2013-06-01"},"publication":"45th Annual ACM Symposium on theory of computing","status":"public","file_date_updated":"2020-07-14T12:45:48Z","date_created":"2018-12-11T11:59:42Z","author":[{"last_name":"Čadek","full_name":"Čadek, Martin","first_name":"Martin"},{"last_name":"Krcál","full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek"},{"first_name":"Jiří","last_name":"Matoušek","full_name":"Matoušek, Jiří"},{"first_name":"Lukáš","last_name":"Vokřínek","full_name":"Vokřínek, Lukáš"},{"full_name":"Wagner, Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"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&quot; (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"}],"date_updated":"2021-01-12T06:59:51Z","oa_version":"Submitted Version","day":"01","ddc":["510"],"title":"Extending continuous maps: Polynomiality and undecidability","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"has_accepted_license":"1"},{"language":[{"iso":"eng"}],"date_published":"2013-06-01T00:00:00Z","publisher":"ACM","doi":"10.1145/2462356.2462373","acknowledgement":"Some of the authors were partially supported by the GIGA ANR grant (contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).","main_file_link":[{"open_access":"1","url":"http://hal.archives-ouvertes.fr/hal-00833791/"}],"date_created":"2018-12-11T11:59:44Z","oa":1,"status":"public","page":"117 - 125","conference":{"end_date":"2013-06-20","name":"SoCG: Symposium on Computational Geometry","location":"Rio de Janeiro, Brazil","start_date":"2013-06-17"},"related_material":{"record":[{"relation":"later_version","id":"1805","status":"public"}]},"publication":"Proceedings of the 29th annual symposium on Computational Geometry","quality_controlled":"1","year":"2013","scopus_import":1,"day":"01","month":"06","title":"Homological reconstruction and simplification in R3","publist_id":"4072","department":[{"_id":"HeEd"}],"_id":"2812","author":[{"full_name":"Attali, Dominique","last_name":"Attali","first_name":"Dominique"},{"last_name":"Bauer","full_name":"Bauer, Ulrich","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"first_name":"Olivier","last_name":"Devillers","full_name":"Devillers, Olivier"},{"first_name":"Marc","full_name":"Glisse, Marc","last_name":"Glisse"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","abstract":[{"lang":"eng","text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard."}],"publication_status":"published","oa_version":"Submitted Version","citation":{"apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., &#38; Lieutier, A. (2013). Homological reconstruction and simplification in R3. In <i>Proceedings of the 29th annual symposium on Computational Geometry</i> (pp. 117–125). Rio de Janeiro, Brazil: ACM. <a href=\"https://doi.org/10.1145/2462356.2462373\">https://doi.org/10.1145/2462356.2462373</a>","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. In: <i>Proceedings of the 29th Annual Symposium on Computational Geometry</i>. ACM; 2013:117-125. doi:<a href=\"https://doi.org/10.1145/2462356.2462373\">10.1145/2462356.2462373</a>","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” in <i>Proceedings of the 29th annual symposium on Computational Geometry</i>, Rio de Janeiro, Brazil, 2013, pp. 117–125.","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” In <i>Proceedings of the 29th Annual Symposium on Computational Geometry</i>, 117–25. ACM, 2013. <a href=\"https://doi.org/10.1145/2462356.2462373\">https://doi.org/10.1145/2462356.2462373</a>.","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” <i>Proceedings of the 29th Annual Symposium on Computational Geometry</i>, ACM, 2013, pp. 117–25, doi:<a href=\"https://doi.org/10.1145/2462356.2462373\">10.1145/2462356.2462373</a>.","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction and simplification in R3. Proceedings of the 29th annual symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 117–125.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125."},"date_updated":"2026-06-18T17:57:27Z"},{"external_id":{"isi":["000320672400005"]},"page":"797 - 822","quality_controlled":"1","year":"2013","oa":1,"publisher":"Springer","doi":"10.1007/s00454-013-9517-x","date_published":"2013-06-01T00:00:00Z","language":[{"iso":"eng"}],"issue":"4","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","citation":{"short":"H. Edelsbrunner, B.T. Fasy, G. Rote, Discrete &#38; Computational Geometry 49 (2013) 797–822.","ista":"Edelsbrunner H, Fasy BT, Rote G. 2013. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete &#38; Computational Geometry. 49(4), 797–822.","chicago":"Edelsbrunner, Herbert, Brittany Terese Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2013. <a href=\"https://doi.org/10.1007/s00454-013-9517-x\">https://doi.org/10.1007/s00454-013-9517-x</a>.","mla":"Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” <i>Discrete &#38; Computational Geometry</i>, vol. 49, no. 4, Springer, 2013, pp. 797–822, doi:<a href=\"https://doi.org/10.1007/s00454-013-9517-x\">10.1007/s00454-013-9517-x</a>.","ieee":"H. Edelsbrunner, B. T. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” <i>Discrete &#38; Computational Geometry</i>, vol. 49, no. 4. Springer, pp. 797–822, 2013.","ama":"Edelsbrunner H, Fasy BT, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. <i>Discrete &#38; Computational Geometry</i>. 2013;49(4):797-822. doi:<a href=\"https://doi.org/10.1007/s00454-013-9517-x\">10.1007/s00454-013-9517-x</a>","apa":"Edelsbrunner, H., Fasy, B. T., &#38; Rote, G. (2013). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-013-9517-x\">https://doi.org/10.1007/s00454-013-9517-x</a>"},"corr_author":"1","volume":49,"type":"journal_article","publist_id":"3991","month":"06","scopus_import":"1","_id":"2815","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"related_material":{"record":[{"status":"public","id":"3134","relation":"earlier_version"}]},"publication":"Discrete & Computational Geometry","main_file_link":[{"url":"https://doi.org/10.1007/s00454-013-9517-x","open_access":"1"}],"date_created":"2018-12-11T11:59:44Z","status":"public","acknowledgement":"This research is partially supported by the National Science Foundation (NSF) under Grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.","article_processing_charge":"No","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Fasy, Brittany Terese","last_name":"Fasy","id":"F65D502E-E68D-11E9-9252-C644099818F6","first_name":"Brittany Terese"},{"full_name":"Rote, Günter","last_name":"Rote","first_name":"Günter"}],"oa_version":"Published Version","intvolume":"        49","date_updated":"2026-06-18T18:35:33Z","abstract":[{"lang":"eng","text":"The fact that a sum of isotropic Gaussian kernels can have more modes than kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally not well studied in higher dimensions. We study a configuration of n+1 Gaussian kernels for which there are exactly n+2 modes. We show that all modes lie on a finite set of lines, which we call axes, and study the restriction of the Gaussian mixture to these axes in order to discover that there are an exponential number of critical points in this configuration. Although the existence of ghost modes remained unknown due to the difficulty of finding examples in ℝ2, we show that the resilience of ghost modes grows like the square root of the dimension. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes."}],"title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","ddc":["500"],"day":"01","isi":1,"department":[{"_id":"HeEd"}]},{"publication":"PNAS","date_created":"2018-12-11T11:59:47Z","main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/"}],"status":"public","article_processing_charge":"No","author":[{"first_name":"Christopher","last_name":"Topp","full_name":"Topp, Christopher"},{"first_name":"Anjali","last_name":"Iyer Pascuzzi","full_name":"Iyer Pascuzzi, Anjali"},{"first_name":"Jill","full_name":"Anderson, Jill","last_name":"Anderson"},{"first_name":"Cheng","last_name":"Lee","full_name":"Lee, Cheng"},{"full_name":"Zurek, Paul","last_name":"Zurek","first_name":"Paul"},{"full_name":"Symonova, Olga","last_name":"Symonova","orcid":"0000-0003-2012-9947","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Zheng","full_name":"Zheng, Ying","first_name":"Ying"},{"first_name":"Alexander","full_name":"Bucksch, Alexander","last_name":"Bucksch"},{"full_name":"Mileyko, Yuriy","last_name":"Mileyko","first_name":"Yuriy"},{"full_name":"Galkovskyi, Taras","last_name":"Galkovskyi","first_name":"Taras"},{"full_name":"Moore, Brad","last_name":"Moore","first_name":"Brad"},{"full_name":"Harer, John","last_name":"Harer","first_name":"John"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Mitchell Olds","full_name":"Mitchell Olds, Thomas","first_name":"Thomas"},{"first_name":"Joshua","full_name":"Weitz, Joshua","last_name":"Weitz"},{"full_name":"Benfey, Philip","last_name":"Benfey","first_name":"Philip"}],"abstract":[{"text":"Identification of genes that control root system architecture in crop plants requires innovations that enable high-throughput and accurate measurements of root system architecture through time. We demonstrate the ability of a semiautomated 3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative genetic basis of root system growth in a rice biparental mapping population, Bala x Azucena. We phenotyped &gt;1,400 3D root models and &gt;57,000 2D images for a suite of 25 traits that quantified the distribution, shape, extent of exploration, and the intrinsic size of root networks at days 12, 14, and 16 of growth in a gellan gum medium. From these data we identified 89 quantitative trait loci, some of which correspond to those found previously in soil-grown plants, and provide evidence for genetic tradeoffs in root growth allocations, such as between the extent and thoroughness of exploration. We also developed a multivariate method for generating and mapping central root architecture phenotypes and used it to identify five major quantitative trait loci (r2 = 24-37%), two of which were not identified by our univariate analysis. Our imaging and analytical platform provides a means to identify genes with high potential for improving root traits and agronomic qualities of crops.","lang":"eng"}],"oa_version":"Submitted Version","date_updated":"2025-09-29T13:57:21Z","intvolume":"       110","day":"30","title":"3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"isi":1,"page":"E1695 - E1704","external_id":{"isi":["000318682300008"],"pmid":["25673779"]},"quality_controlled":"1","year":"2013","date_published":"2013-04-30T00:00:00Z","doi":"10.1073/pnas.1304354110","publisher":"National Academy of Sciences","language":[{"iso":"eng"}],"issue":"18","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","volume":110,"publication_status":"published","citation":{"mla":"Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” <i>PNAS</i>, vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:<a href=\"https://doi.org/10.1073/pnas.1304354110\">10.1073/pnas.1304354110</a>.","chicago":"Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” <i>PNAS</i>. National Academy of Sciences, 2013. <a href=\"https://doi.org/10.1073/pnas.1304354110\">https://doi.org/10.1073/pnas.1304354110</a>.","ista":"Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y, Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 110(18), E1695–E1704.","short":"C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y. Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner, T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704.","apa":"Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O., … Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. <i>PNAS</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.1304354110\">https://doi.org/10.1073/pnas.1304354110</a>","ama":"Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. <i>PNAS</i>. 2013;110(18):E1695-E1704. doi:<a href=\"https://doi.org/10.1073/pnas.1304354110\">10.1073/pnas.1304354110</a>","ieee":"C. Topp <i>et al.</i>, “3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture,” <i>PNAS</i>, vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013."},"pmid":1,"scopus_import":"1","month":"04","publist_id":"3979","_id":"2822"}]