{"status":"public","related_material":{"record":[{"relation":"earlier_version","id":"9296","status":"public"}]},"quality_controlled":"1","title":"On compatible matchings","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2022-08-21T22:01:56Z","oa_version":"Published Version","oa":1,"scopus_import":"1","publisher":"Brown University","issue":"2","publication_status":"published","date_published":"2022-06-01T00:00:00Z","abstract":[{"lang":"eng","text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge."}],"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"day":"01","type":"journal_article","file":[{"date_updated":"2022-08-22T06:42:42Z","success":1,"file_id":"11940","date_created":"2022-08-22T06:42:42Z","file_size":694538,"checksum":"dc6e255e3558faff924fd9e370886c11","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf"}],"date_updated":"2023-02-23T13:54:21Z","tmp":{"image":"/images/cc_by.png","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"},"month":"06","article_processing_charge":"No","acknowledgement":"A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","file_date_updated":"2022-08-22T06:42:42Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"},{"name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23"},{"call_identifier":"FWF","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory"}],"ddc":["000"],"volume":26,"intvolume":"        26","year":"2022","citation":{"ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” <i>Journal of Graph Algorithms and Applications</i>. Brown University, 2022. <a href=\"https://doi.org/10.7155/jgaa.00591\">https://doi.org/10.7155/jgaa.00591</a>.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. <i>Journal of Graph Algorithms and Applications</i>. Brown University. <a href=\"https://doi.org/10.7155/jgaa.00591\">https://doi.org/10.7155/jgaa.00591</a>","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. <i>Journal of Graph Algorithms and Applications</i>. 2022;26(2):225-240. doi:<a href=\"https://doi.org/10.7155/jgaa.00591\">10.7155/jgaa.00591</a>","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” <i>Journal of Graph Algorithms and Applications</i>, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:<a href=\"https://doi.org/10.7155/jgaa.00591\">10.7155/jgaa.00591</a>.","ieee":"O. Aichholzer <i>et al.</i>, “On compatible matchings,” <i>Journal of Graph Algorithms and Applications</i>, vol. 26, no. 2. Brown University, pp. 225–240, 2022."},"article_type":"original","ec_funded":1,"_id":"11938","language":[{"iso":"eng"}],"publication":"Journal of Graph Algorithms and Applications","has_accepted_license":"1","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"orcid":"0000-0003-2401-8670","last_name":"Arroyo Guevara","first_name":"Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","full_name":"Arroyo Guevara, Alan M"},{"orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Irene","last_name":"Parada","full_name":"Parada, Irene"},{"full_name":"Perz, Daniel","last_name":"Perz","first_name":"Daniel"},{"full_name":"Pilz, Alexander","last_name":"Pilz","first_name":"Alexander"},{"full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684"},{"full_name":"Vogtenhuber, Birgit","first_name":"Birgit","last_name":"Vogtenhuber"}],"page":"225-240","doi":"10.7155/jgaa.00591","publication_identifier":{"issn":["1526-1719"]},"external_id":{"arxiv":["2101.03928"]}}