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This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2024-01-29T09:45:06Z","type":"conference","conference":{"location":"Isola delle Femmine, Palermo, Italy","end_date":"2023-09-22","start_date":"2023-09-20","name":"GD: Graph Drawing and Network Visualization"},"status":"public","_id":"14888","page":"18-33","doi":"10.1007/978-3-031-49275-4_2","date_published":"2024-01-06T00:00:00Z","date_created":"2024-01-28T23:01:43Z","year":"2024","day":"06","publication":"31st International Symposium on Graph Drawing and Network Visualization","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].","author":[{"first_name":"Phoebe","full_name":"De Nooijer, Phoebe","last_name":"De Nooijer"},{"first_name":"Soeren","full_name":"Terziadis, Soeren","last_name":"Terziadis"},{"first_name":"Alexandra","full_name":"Weinberger, Alexandra","last_name":"Weinberger"},{"last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mchedlidze, Tamara","last_name":"Mchedlidze","first_name":"Tamara"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"last_name":"Rote","full_name":"Rote, Günter","first_name":"Günter"}],"article_processing_charge":"No","external_id":{"arxiv":["2202.12175"]},"title":"Removing popular faces in curve arrangements","citation":{"chicago":"De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In 31st International Symposium on Graph Drawing and Network Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2.","ista":"De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33.","mla":"De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.","short":"P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33.","ieee":"P. De Nooijer et al., “Removing popular faces in curve arrangements,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.","apa":"De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49275-4_2","ama":"De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"_id":"15012","conference":{"start_date":"2023-09-20","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy","name":"GD: Graph Drawing and Network Visualization"},"type":"conference","status":"public","date_updated":"2024-02-20T09:13:07Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.13201"}],"scopus_import":"1","alternative_title":["LNCS"],"intvolume":" 14465","month":"01","publication_status":"published","publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783031492716"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":14465,"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"citation":{"short":"J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346.","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14465. Springer Nature; 2024:339-346. doi:10.1007/978-3-031-49272-3_23","apa":"Pach, J., Saghafian, M., & Schnider, P. (2024). Decomposition of geometric graphs into star-forests. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14465, pp. 339–346). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49272-3_23","mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14465, Springer Nature, 2024, pp. 339–46, doi:10.1007/978-3-031-49272-3_23.","ista":"Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs into star-forests. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.","chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” In 31st International Symposium on Graph Drawing and Network Visualization, 14465:339–46. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49272-3_23."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2306.13201"]},"article_processing_charge":"No","author":[{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","full_name":"Pach, János","last_name":"Pach"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza"},{"first_name":"Patrick","last_name":"Schnider","full_name":"Schnider, Patrick"}],"title":"Decomposition of geometric graphs into star-forests","acknowledgement":"János Pach’s Research partially supported by European Research Council (ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH), grant K-131529. Work by Morteza Saghafian is partially supported by the European Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2024","publication":"31st International Symposium on Graph Drawing and Network Visualization","day":"01","page":"339-346","date_created":"2024-02-18T23:01:03Z","doi":"10.1007/978-3-031-49272-3_23","date_published":"2024-01-01T00:00:00Z"},{"publisher":"Institute of Science and Technology Austria","oa":1,"page":"108","date_published":"2024-03-08T00:00:00Z","doi":"10.15479/at:ista:15094","date_created":"2024-03-08T15:28:10Z","has_accepted_license":"1","year":"2024","day":"08","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"}],"article_processing_charge":"No","title":"Persistence and Morse theory for discrete geometric structures","citation":{"ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria.","chicago":"Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15094.","short":"S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.","ieee":"S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024.","apa":"Cultrera di Montesano, S. (2024). Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15094","ama":"Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:10.15479/at:ista:15094","mla":"Cultrera di Montesano, Sebastiano. Persistence and Morse Theory for Discrete Geometric Structures. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15094."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","alternative_title":["ISTA Thesis"],"month":"03","abstract":[{"lang":"eng","text":"Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in\r\ndiscrete geometry that have captivated mathematicians for centuries, if not millennia. This\r\nthesis seeks to cast new light on these structures by illustrating specific instances where a\r\ntopological perspective, specifically through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt first glance, the topology of these geometric objects might seem uneventful: point sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which\r\nis a contractible space, and the topology of a network primarily involves the enumeration\r\nof connected components and cycles within the network. However, beneath this apparent\r\nsimplicity, there lies an array of intriguing structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused on three case studies, each addressing one of the mentioned objects, this work\r\nwill showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry, algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n"}],"oa_version":"Published Version","related_material":{"record":[{"status":"public","id":"11660","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"11658","status":"public"},{"id":"13182","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"15090"},{"status":"public","id":"15091","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"15093","status":"public"}]},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","ec_funded":1,"publication_identifier":{"issn":["2663 - 337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"file_id":"15112","checksum":"1e468bfa42a7dcf04d89f4dadc621c87","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2024-03-14T08:55:07Z","file_name":"Thesis Sebastiano.pdf","creator":"scultrer","date_updated":"2024-03-14T08:55:07Z","file_size":4106872},{"checksum":"bcbd213490f5a7e68855a092bbce93f1","file_id":"15113","content_type":"application/zip","access_level":"closed","relation":"source_file","date_created":"2024-03-14T08:56:24Z","file_name":"Thesis (1).zip","date_updated":"2024-03-14T14:14:35Z","file_size":4746234,"creator":"scultrer"}],"language":[{"iso":"eng"}],"type":"dissertation","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"status":"public","_id":"15094","file_date_updated":"2024-03-14T14:14:35Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"supervisor":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2024-03-20T09:36:57Z","ddc":["514","500","516"]},{"oa":1,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","acknowledgement":"The first and second authors are funded by the European Research Council under the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research and innovation programme, ERC grant no. 101019564, “The Design of Modern Fully Dynamic DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35.","date_created":"2024-03-08T10:27:39Z","date_published":"2024-01-04T00:00:00Z","doi":"10.1137/1.9781611977912.11","page":"243 - 295","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","day":"04","year":"2024","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"The Wittgenstein Prize","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564"},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422","name":"Wittgenstein Award - Monika Henzinger"},{"grant_number":"P33775 ","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"title":"Dynamically maintaining the persistent homology of time series","editor":[{"first_name":"David P.","last_name":"Woodruff","full_name":"Woodruff, David P."}],"external_id":{"arxiv":["2311.01115"]},"article_processing_charge":"No","author":[{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"last_name":"Ost","full_name":"Ost, Lara","first_name":"Lara"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"apa":"Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M. H., & Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.11","ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics; 2024:243-295. doi:10.1137/1.9781611977912.11","short":"S. Cultrera di Montesano, H. Edelsbrunner, M.H. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.","ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. H. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Alexandria, VA, USA, 2024, pp. 243–295.","mla":"Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:10.1137/1.9781611977912.11.","ista":"Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorigthms, 243–295.","chicago":"Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika H Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.11."},"month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2311.01115"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right."}],"ec_funded":1,"related_material":{"record":[{"id":"15094","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eisbn":["9781611977912"]},"status":"public","conference":{"name":"SODA: Symposium on Discrete Algorigthms","start_date":"2024-01-07","end_date":"2024-01-10","location":"Alexandria, VA, USA"},"type":"conference","_id":"15093","department":[{"_id":"HeEd"},{"_id":"MoHe"}],"date_updated":"2024-03-20T09:36:56Z"},{"related_material":{"record":[{"status":"public","id":"15094","relation":"dissertation_contains"}]},"date_published":"2024-02-07T00:00:00Z","date_created":"2024-03-08T10:13:59Z","day":"07","publication":"arXiv","language":[{"iso":"eng"}],"publication_status":"submitted","year":"2024","month":"02","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03128"}],"oa":1,"oa_version":"Preprint","abstract":[{"text":"Motivated by applications in the medical sciences, we study finite chromatic\r\nsets in Euclidean space from a topological perspective. Based on the persistent\r\nhomology for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers that describe the geometric micro- and macro-structure\r\nof how the color classes mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay and alpha complexes, and code that does these\r\ncomputations is provided.","lang":"eng"}],"department":[{"_id":"HeEd"}],"title":"Chromatic alpha complexes","author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","last_name":"Draganov","full_name":"Draganov, Ondrej"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"external_id":{"arxiv":["2212.03128"]},"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). Chromatic alpha complexes. arXiv.","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” arXiv. .","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” ArXiv, 2212.03128.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv, 2212.03128.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” ArXiv, n.d."},"date_updated":"2024-03-20T09:36:56Z","status":"public","type":"preprint","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"2212.03128","_id":"15091"}]