[{"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Tamal K.","last_name":"Dey","full_name":"Dey, Tamal K."},{"first_name":"Michał","last_name":"Lipiński","full_name":"Lipiński, Michał","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","orcid":"0000-0001-9789-9750"},{"last_name":"Soriano Trigueros","first_name":"Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","full_name":"Soriano Trigueros, Manuel","orcid":"0000-0003-2449-1433"}],"title":"Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations","article_processing_charge":"Yes (via OA deal)","ddc":["500"],"publication":"Foundations of Computational Mathematics","das_tickbox":"0","oa_version":"Published Version","date_updated":"2026-08-11T06:13:33Z","OA_place":"publisher","researchdata_availability":"no","main_file_link":[{"url":"https://doi.org/10.1007/s10208-026-09766-6","open_access":"1"}],"project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"doi":"10.1007/s10208-026-09766-6","keyword":["Multivector field","Conley index","Morse decomposition","Bifurcation","Continuation","Zigzag persistence","Persistence barcode","Gentle algebra"],"quality_controlled":"1","oa":1,"article_type":"original","day":"04","citation":{"ista":"Dey TK, Lipiński M, Soriano Trigueros M. 2026. Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. Foundations of Computational Mathematics.","apa":"Dey, T. K., Lipiński, M., &#38; Soriano Trigueros, M. (2026). Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-026-09766-6\">https://doi.org/10.1007/s10208-026-09766-6</a>","ama":"Dey TK, Lipiński M, Soriano Trigueros M. Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. <i>Foundations of Computational Mathematics</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s10208-026-09766-6\">10.1007/s10208-026-09766-6</a>","ieee":"T. K. Dey, M. Lipiński, and M. Soriano Trigueros, “Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations,” <i>Foundations of Computational Mathematics</i>. Springer, 2026.","short":"T.K. Dey, M. Lipiński, M. Soriano Trigueros, Foundations of Computational Mathematics (2026).","chicago":"Dey, Tamal K., Michał Lipiński, and Manuel Soriano Trigueros. “Conley-Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” <i>Foundations of Computational Mathematics</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s10208-026-09766-6\">https://doi.org/10.1007/s10208-026-09766-6</a>.","mla":"Dey, Tamal K., et al. “Conley-Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” <i>Foundations of Computational Mathematics</i>, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s10208-026-09766-6\">10.1007/s10208-026-09766-6</a>."},"publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"year":"2026","OA_type":"hybrid","date_created":"2026-08-05T06:11:30Z","abstract":[{"lang":"eng","text":"Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems—a young but already well-established theory. We introduce the Conley–Morse persistence barcode, a compact algebraic descriptor of combinatorial bifurcations. This barcode captures structural changes in a dynamical system at the level of Morse decompositions and provides a characterization of the nature of observed transitions in terms of the Conley index. The construction of the Conley–Morse persistence barcode builds upon ideas from topological persistence. Specifically, we consider a persistence module obtained from the Conley index of invariant sets indexed over a poset. Using gentle algebras, we prove that this module decomposes into simple intervals (bars) and compute them by adapting the zigzag persistence algorithm to our purpose."}],"external_id":{"arxiv":["2504.17105"]},"publisher":"Springer","has_accepted_license":"1","publication_status":"epub_ahead","month":"08","_id":"22648","supplementarymaterial":"yes","arxiv":1,"fulldoi":"https://doi.org/10.1007/s10208-026-09766-6","ec_funded":1,"PlanS_conform":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"status":"public","language":[{"iso":"eng"}],"scopus_import":"1","department":[{"_id":"HeEd"}],"corr_author":"1","acknowledgement":"M.L. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. T.D. acknowledges the support of NSF funds CCF-2437030 and DMS-2301360. The authors would like to thank the anonymous reviewers for their careful reading of the paper. Their feedback significantly improved the quality of the article. T.D. and M.L. would like to acknowledge many thought-provoking discussions with Marian Mrozek on combinatorial dynamical systems and their continuations. M.S.T. would like to thank Álvaro Sánchez for insightful discussions about representation theory. Open access funding provided by Institute of Science and Technology (IST Austria).","date_published":"2026-08-04T00:00:00Z"},{"_id":"23155","month":"10","external_id":{"arxiv":["2505.22875"]},"publisher":"Institute of Mathematical Statistics","file":[{"file_name":"2026_AnnalsAppliedProbability_Hollom.pdf","access_level":"open_access","file_id":"23165","creator":"dernst","success":1,"date_created":"2026-10-19T07:33:58Z","date_updated":"2026-10-19T07:33:58Z","content_type":"application/pdf","file_size":320593,"checksum":"46101e61d29cf40f0a204801d15a848f","relation":"main_file"}],"has_accepted_license":"1","publication_status":"published","year":"2026","OA_type":"hybrid","date_created":"2026-10-18T22:01:52Z","abstract":[{"text":"In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we\r\nshow that, for a wide range of parameters d1 ≤ d2, there exists a coupling of\r\nG(n,d1) and G(n,d2) satisfying that G(n,d1) ⊆ G(n,d2) with high probability, confirming a conjecture of Gao, Isaev and McKay in a new regime.\r\nOur contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for\r\ngenerating unions of random edge-disjoint perfect matchings, and refined estimates of Gao’s bounds on the number of perfect matchings in random regular graphs. In addition, we make progress towards another conjecture of Isaev,\r\nMcKay, Southwell and Zhukovskii.","lang":"eng"}],"publication_identifier":{"eissn":["2168-8737"],"issn":["1050-5164"]},"department":[{"_id":"MaKw"},{"_id":"GradSch"}],"scopus_import":"1","acknowledgement":"We are grateful to Béla Bollobás, to Matthew Kwan and to Fabio\r\nToninelli for their helpful comments and suggestions, and to Nicholas Wormald for useful\r\nremarks on a preliminary version of this work and pointing us towards the reference [29].\r\nThe authors would also like to thank several anonymous referees for many useful suggestions,\r\nincluding pointing out that Lemma 2.10 already appeared in [11].\r\nPart of this research was done during a visit of the fourth author to IST Austria. We thank\r\nIST Austria for its hospitality.\r\nFor open access purposes, the authors have applied a CC BY public copyright license to\r\nany author accepted manuscript version arising from this submission. L. Hollom was supported by the Internal Graduate Studentship of Trinity College, Cambridge.\r\nL. Lichev was supported by the Austrian Science Fund (FWF) grant No. 10.55776/ESP624.\r\nA. Mond was supported by UK Research and Innovation grant MR/W007320/2. Wang was\r\nsupported by the ERC Starting Grant “RANDSTRUCT” No. 101076777.","date_published":"2026-10-01T00:00:00Z","status":"public","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1214/26-AAP2345","issue":"5","PlanS_conform":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"supplementarymaterial":"no","arxiv":1,"OA_place":"publisher","file_date_updated":"2026-10-19T07:33:58Z","mathsc":["05C80"],"researchdata_availability":"no","das_tickbox":"0","date_updated":"2026-10-19T07:39:17Z","oa_version":"Published Version","ddc":["500"],"publication":"Annals of Applied Probability","volume":36,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","author":[{"full_name":"Hollom, Lawrence","last_name":"Hollom","first_name":"Lawrence"},{"first_name":"Lyuben","last_name":"Lichev","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","full_name":"Lichev, Lyuben"},{"first_name":"Adva","last_name":"Mond","full_name":"Mond, Adva"},{"full_name":"Portier, Julien","first_name":"Julien","last_name":"Portier"},{"last_name":"Wang","first_name":"Yiting","id":"1917d194-076e-11ed-97cd-837255f88785","full_name":"Wang, Yiting"}],"title":"Monotonicity and decompositions of random regular graphs","article_processing_charge":"Yes (in subscription journal)","citation":{"ieee":"L. Hollom, L. Lichev, A. Mond, J. Portier, and Y. Wang, “Monotonicity and decompositions of random regular graphs,” <i>Annals of Applied Probability</i>, vol. 36, no. 5. Institute of Mathematical Statistics, pp. 4716–4738, 2026.","chicago":"Hollom, Lawrence, Lyuben Lichev, Adva Mond, Julien Portier, and Yiting Wang. “Monotonicity and Decompositions of Random Regular Graphs.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2026. <a href=\"https://doi.org/10.1214/26-AAP2345\">https://doi.org/10.1214/26-AAP2345</a>.","short":"L. Hollom, L. Lichev, A. Mond, J. Portier, Y. Wang, Annals of Applied Probability 36 (2026) 4716–4738.","mla":"Hollom, Lawrence, et al. “Monotonicity and Decompositions of Random Regular Graphs.” <i>Annals of Applied Probability</i>, vol. 36, no. 5, Institute of Mathematical Statistics, 2026, pp. 4716–38, doi:<a href=\"https://doi.org/10.1214/26-AAP2345\">10.1214/26-AAP2345</a>.","ista":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. 2026. Monotonicity and decompositions of random regular graphs. Annals of Applied Probability. 36(5), 4716–4738.","apa":"Hollom, L., Lichev, L., Mond, A., Portier, J., &#38; Wang, Y. (2026). Monotonicity and decompositions of random regular graphs. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/26-AAP2345\">https://doi.org/10.1214/26-AAP2345</a>","ama":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. Monotonicity and decompositions of random regular graphs. <i>Annals of Applied Probability</i>. 2026;36(5):4716-4738. doi:<a href=\"https://doi.org/10.1214/26-AAP2345\">10.1214/26-AAP2345</a>"},"page":"4716-4738","article_type":"original","day":"01","quality_controlled":"1","oa":1,"intvolume":"        36","project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"},{"_id":"e19fef4c-1f3d-11f0-ac04-b8b1af6886d8","name":"THRESHOLDS IN SEMI-RANDOM PROCESSES AND GRAPH EMBEDDINGS","grant_number":"E624"}],"keyword":["Random regular graphs","coupling","contiguity","total variation distance","decomposition"],"doi":"10.1214/26-AAP2345"},{"volume":"P-377","publication":"Software Engineering 2026","ddc":["000"],"article_processing_charge":"No","title":"Off-the-Shelf cooperative software verification by splitting programs dynamically","author":[{"full_name":"Richter, Cedric","last_name":"Richter","first_name":"Cedric"},{"full_name":"Chalupa, Marek","id":"87e34708-d6c6-11ec-9f5b-9391e7be2463","last_name":"Chalupa","first_name":"Marek"},{"last_name":"Jakobs","first_name":"Marie Christine","full_name":"Jakobs, Marie Christine"},{"first_name":"Heike","last_name":"Wehrheim","full_name":"Wehrheim, Heike"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","conference":{"end_date":"2026-02-27","location":"Bonn, Switzerland","name":"SE: Software Engineering","start_date":"2026-02-23"},"researchdata_availability":"yes","file_date_updated":"2026-10-19T08:39:37Z","OA_place":"publisher","date_updated":"2026-10-19T08:49:32Z","alternative_title":["Lecture Notes in Informatics"],"das_tickbox":"1","oa_version":"Published Version","oa":1,"quality_controlled":"1","dataavailabilitystatement":"All our implementations and data are archived and available at Zenodo5\r\nand are evaluated as an artifact in the ICSE 2025 artifact evaluation. Furthermore, our\r\napproach is integrated into the software verifier Bubaak [CR25] which we submitted as\r\npart of our contribution to SV-COMP 2025.","license":"https://creativecommons.org/licenses/by-sa/4.0/","keyword":["Software Verification","Cooperation","Program Decomposition"],"doi":"10.18420/se2026_45","citation":{"ista":"Richter C, Chalupa M, Jakobs MC, Wehrheim H. 2026. Off-the-Shelf cooperative software verification by splitting programs dynamically. Software Engineering 2026. SE: Software Engineering, Lecture Notes in Informatics, vol. P-377, 41–42.","apa":"Richter, C., Chalupa, M., Jakobs, M. C., &#38; Wehrheim, H. (2026). Off-the-Shelf cooperative software verification by splitting programs dynamically. In <i>Software Engineering 2026</i> (Vol. P-377, pp. 41–42). Bonn, Switzerland: Gesellschaft für Informatik. <a href=\"https://doi.org/10.18420/se2026_45\">https://doi.org/10.18420/se2026_45</a>","ama":"Richter C, Chalupa M, Jakobs MC, Wehrheim H. Off-the-Shelf cooperative software verification by splitting programs dynamically. In: <i>Software Engineering 2026</i>. Vol P-377. Gesellschaft für Informatik; 2026:41-42. doi:<a href=\"https://doi.org/10.18420/se2026_45\">10.18420/se2026_45</a>","ieee":"C. Richter, M. Chalupa, M. C. Jakobs, and H. Wehrheim, “Off-the-Shelf cooperative software verification by splitting programs dynamically,” in <i>Software Engineering 2026</i>, Bonn, Switzerland, 2026, vol. P-377, pp. 41–42.","chicago":"Richter, Cedric, Marek Chalupa, Marie Christine Jakobs, and Heike Wehrheim. “Off-the-Shelf Cooperative Software Verification by Splitting Programs Dynamically.” In <i>Software Engineering 2026</i>, P-377:41–42. Gesellschaft für Informatik, 2026. <a href=\"https://doi.org/10.18420/se2026_45\">https://doi.org/10.18420/se2026_45</a>.","short":"C. Richter, M. Chalupa, M.C. Jakobs, H. Wehrheim, in:, Software Engineering 2026, Gesellschaft für Informatik, 2026, pp. 41–42.","mla":"Richter, Cedric, et al. “Off-the-Shelf Cooperative Software Verification by Splitting Programs Dynamically.” <i>Software Engineering 2026</i>, vol. P-377, Gesellschaft für Informatik, 2026, pp. 41–42, doi:<a href=\"https://doi.org/10.18420/se2026_45\">10.18420/se2026_45</a>."},"day":"01","page":"41-42","abstract":[{"lang":"eng","text":"Cooperative software verification aims at improving the effectiveness and efficiency of software verification by enabling multiple verification tools to work together. Existing cooperative verification schemes, however, typically require specialized interfaces or tight integration, limiting their practical applicability. In our International Conference on Software Engineering (ICSE) 2025 publication, we introduce dynamic program splitting – a novel approach that enables cooperation between off-the-shelf verification tools without requiring any modifications. The key idea is to probe verification tools on a given verification task under a time limit and split tasks dynamically that cannot be verified under the given time constraints. The process continues recursively, incrementally identifying program parts that are particularly hard for the given verifier. The remaining unverified parts are provided to a second verifier, allowing to leverage the complementary strengths of different tools. Our evaluation on SV-COMP benchmarks demonstrates that cooperation through dynamic program splitting enables the verification of tasks that none of the individual verifiers can solve on their own."}],"date_created":"2026-08-02T22:01:54Z","OA_type":"hybrid","year":"2026","publication_identifier":{"eissn":["1617-5468"]},"month":"03","_id":"22622","publication_status":"published","has_accepted_license":"1","publisher":"Gesellschaft für Informatik","file":[{"date_created":"2026-10-19T08:39:37Z","success":1,"creator":"dernst","file_id":"23170","access_level":"open_access","file_name":"2026_LNI_Richter.pdf","relation":"main_file","checksum":"3371c63711ed26efa41744834d337d28","file_size":147208,"content_type":"application/pdf","date_updated":"2026-10-19T08:39:37Z"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","short":"CC BY-SA (4.0)"},"fulldoi":"https://doi.org/10.18420/se2026_45","supplementarymaterial":"no","date_published":"2026-03-01T00:00:00Z","department":[{"_id":"ToHe"}],"scopus_import":"1","language":[{"iso":"eng"}],"status":"public"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"isi":1,"ec_funded":1,"arxiv":1,"department":[{"_id":"ToHe"}],"date_published":"2020-10-01T00:00:00Z","status":"public","language":[{"iso":"eng"}],"year":"2020","abstract":[{"text":"Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.","lang":"eng"}],"date_created":"2020-08-24T12:56:20Z","month":"10","_id":"8287","file":[{"creator":"cschilli","success":1,"date_created":"2020-08-24T12:53:15Z","file_name":"2020EMSOFT.pdf","access_level":"open_access","file_id":"8288","file_size":696384,"checksum":"d19e97d0f8a3a441dc078ec812297d75","relation":"main_file","date_updated":"2020-08-24T12:53:15Z","content_type":"application/pdf"}],"external_id":{"isi":["000587712700072"],"arxiv":["1905.02458"]},"publication_status":"published","has_accepted_license":"1","quality_controlled":"1","oa":1,"project":[{"name":"Rigorous Systems Engineering","grant_number":"S 11407_N23","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00312","name":"Synaptic communication in neuronal microcircuits","call_identifier":"FWF","_id":"25C5A090-B435-11E9-9278-68D0E5697425"},{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"keyword":["reachability","hybrid systems","decomposition"],"citation":{"mla":"Bogomolov, Sergiy, et al. “Reachability Analysis of Linear Hybrid Systems via Block Decomposition.” <i>Proceedings of the International Conference on Embedded Software</i>, 2020.","short":"S. Bogomolov, M. Forets, G. Frehse, K. Potomkin, C. Schilling, in:, Proceedings of the International Conference on Embedded Software, 2020.","chicago":"Bogomolov, Sergiy, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, and Christian Schilling. “Reachability Analysis of Linear Hybrid Systems via Block Decomposition.” In <i>Proceedings of the International Conference on Embedded Software</i>, 2020.","ieee":"S. Bogomolov, M. Forets, G. Frehse, K. Potomkin, and C. Schilling, “Reachability analysis of linear hybrid systems via block decomposition,” in <i>Proceedings of the International Conference on Embedded Software</i>, Virtual , 2020.","ama":"Bogomolov S, Forets M, Frehse G, Potomkin K, Schilling C. Reachability analysis of linear hybrid systems via block decomposition. In: <i>Proceedings of the International Conference on Embedded Software</i>. ; 2020.","apa":"Bogomolov, S., Forets, M., Frehse, G., Potomkin, K., &#38; Schilling, C. (2020). Reachability analysis of linear hybrid systems via block decomposition. In <i>Proceedings of the International Conference on Embedded Software</i>. Virtual .","ista":"Bogomolov S, Forets M, Frehse G, Potomkin K, Schilling C. 2020. Reachability analysis of linear hybrid systems via block decomposition. Proceedings of the International Conference on Embedded Software. EMSOFT: Embedded Software."},"day":"01","ddc":["000"],"publication":"Proceedings of the International Conference on Embedded Software","title":"Reachability analysis of linear hybrid systems via block decomposition","author":[{"last_name":"Bogomolov","first_name":"Sergiy","full_name":"Bogomolov, Sergiy"},{"last_name":"Forets","first_name":"Marcelo","full_name":"Forets, Marcelo"},{"full_name":"Frehse, Goran","last_name":"Frehse","first_name":"Goran"},{"last_name":"Potomkin","first_name":"Kostiantyn","full_name":"Potomkin, Kostiantyn"},{"orcid":"0000-0003-3658-1065","last_name":"Schilling","first_name":"Christian","id":"3A2F4DCE-F248-11E8-B48F-1D18A9856A87","full_name":"Schilling, Christian"}],"conference":{"start_date":"2020-09-20","name":"EMSOFT: Embedded Software","location":"Virtual ","end_date":"2020-09-25"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"conference","article_processing_charge":"No","file_date_updated":"2020-08-24T12:53:15Z","related_material":{"record":[{"relation":"later_version","id":"8790","status":"public"}]},"oa_version":"Preprint","date_updated":"2026-04-03T09:32:00Z"},{"publication_status":"published","publisher":"Springer","_id":"4097","month":"01","publication_identifier":{"isbn":["978-3-540-19488-0"]},"date_created":"2018-12-11T12:06:55Z","abstract":[{"text":"Arrangements of curves in the plane are of fundamental significance in many problems of computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of (some weaker variant of) that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.","lang":"eng"}],"year":"1988","publist_id":"2028","language":[{"iso":"eng"}],"status":"public","acknowledgement":"Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under grant CCR-8714566. Work on this paper by the third and sixth authors has been supported by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation. Work by the sixth author has also been supported by a research grant from the NCRD — the Israeli National Council for Research and Development. Work by the fourth author has been supported by National Science Foundation Grant DMS-8501947.","date_published":"1988-01-01T00:00:00Z","scopus_import":"1","fulldoi":"https://doi.org/10.1007/3-540-19488-6_118","oa_version":"None","alternative_title":["LNCS"],"date_updated":"2022-02-08T10:15:09Z","article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","conference":{"name":"ICALP: Automata, Languages and Programming","start_date":"1988-07-11","end_date":"1988-07-15","location":"Tampere, Finland"},"type":"conference","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János"},{"full_name":"Pollack, Richard","last_name":"Pollack","first_name":"Richard"},{"full_name":"Seidel, Raimund","last_name":"Seidel","first_name":"Raimund"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"}],"title":"Arrangements of curves in the plane - topology, combinatorics, and algorithms","publication":"15th International Colloquium on Automata, Languages and Programming","volume":317,"day":"01","page":"214 - 229","extern":"1","citation":{"ista":"Edelsbrunner H, Guibas L, Pach J, Pollack R, Seidel R, Sharir M. 1988. Arrangements of curves in the plane - topology, combinatorics, and algorithms. 15th International Colloquium on Automata, Languages and Programming. ICALP: Automata, Languages and Programming, LNCS, vol. 317, 214–229.","ama":"Edelsbrunner H, Guibas L, Pach J, Pollack R, Seidel R, Sharir M. Arrangements of curves in the plane - topology, combinatorics, and algorithms. In: <i>15th International Colloquium on Automata, Languages and Programming</i>. Vol 317. Springer; 1988:214-229. doi:<a href=\"https://doi.org/10.1007/3-540-19488-6_118\">10.1007/3-540-19488-6_118</a>","apa":"Edelsbrunner, H., Guibas, L., Pach, J., Pollack, R., Seidel, R., &#38; Sharir, M. (1988). Arrangements of curves in the plane - topology, combinatorics, and algorithms. In <i>15th International Colloquium on Automata, Languages and Programming</i> (Vol. 317, pp. 214–229). Tampere, Finland: Springer. <a href=\"https://doi.org/10.1007/3-540-19488-6_118\">https://doi.org/10.1007/3-540-19488-6_118</a>","ieee":"H. Edelsbrunner, L. Guibas, J. Pach, R. Pollack, R. Seidel, and M. Sharir, “Arrangements of curves in the plane - topology, combinatorics, and algorithms,” in <i>15th International Colloquium on Automata, Languages and Programming</i>, Tampere, Finland, 1988, vol. 317, pp. 214–229.","mla":"Edelsbrunner, Herbert, et al. “Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms.” <i>15th International Colloquium on Automata, Languages and Programming</i>, vol. 317, Springer, 1988, pp. 214–29, doi:<a href=\"https://doi.org/10.1007/3-540-19488-6_118\">10.1007/3-540-19488-6_118</a>.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, János Pach, Richard Pollack, Raimund Seidel, and Micha Sharir. “Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms.” In <i>15th International Colloquium on Automata, Languages and Programming</i>, 317:214–29. Springer, 1988. <a href=\"https://doi.org/10.1007/3-540-19488-6_118\">https://doi.org/10.1007/3-540-19488-6_118</a>.","short":"H. Edelsbrunner, L. Guibas, J. Pach, R. Pollack, R. Seidel, M. Sharir, in:, 15th International Colloquium on Automata, Languages and Programming, Springer, 1988, pp. 214–229."},"doi":"10.1007/3-540-19488-6_118","keyword":["line segment","computational geometry","Jordan curve","cell decomposition","vertical tangency"],"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-19488-6_118"}],"intvolume":"       317","quality_controlled":"1"}]