{"page":"221-233","oa_version":"Preprint","oa":1,"external_id":{"arxiv":["2101.03928"]},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","abstract":[{"text":" 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 convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ 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(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.","lang":"eng"}],"publisher":"Springer Nature","intvolume":" 12635","publication_identifier":{"isbn":["9783030682101"],"eissn":["16113349"],"issn":["03029743"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.03928"}],"year":"2021","language":[{"iso":"eng"}],"date_updated":"2023-02-21T16:33:44Z","day":"16","ec_funded":1,"doi":"10.1007/978-3-030-68211-8_18","publication":"15th International Conference on Algorithms and Computation","conference":{"start_date":"2021-02-28","location":"Yangon, Myanmar","name":"WALCOM: Algorithms and Computation","end_date":"2021-03-02"},"scopus_import":"1","acknowledgement":"A.A. funded by the Marie Skłodowska-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).","date_created":"2021-03-28T22:01:41Z","date_published":"2021-02-16T00:00:00Z","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF","name":"The Wittgenstein Prize"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","call_identifier":"FP7"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"S11407","name":"Game Theory"}],"title":"On compatible matchings","citation":{"ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233.","ieee":"O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233."},"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","first_name":"Alan M","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"full_name":"Perz, Daniel","first_name":"Daniel","last_name":"Perz"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","first_name":"Josef"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"month":"02","related_material":{"record":[{"status":"public","id":"11938","relation":"later_version"}]},"volume":12635,"publication_status":"published","quality_controlled":"1","_id":"9296","status":"public","article_processing_charge":"No","alternative_title":["LNCS"],"type":"conference","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}]}