{"issue":"6","publication":"Journal of Graph Algorithms and Applications","external_id":{"arxiv":["2109.14892"]},"publisher":"Brown University","publication_status":"published","date_created":"2023-08-06T22:01:11Z","month":"07","_id":"13969","file":[{"file_size":865774,"creator":"dernst","access_level":"open_access","date_updated":"2023-08-07T08:00:48Z","success":1,"date_created":"2023-08-07T08:00:48Z","checksum":"9c30d2b8e324cc1c904f2aeec92013a3","file_name":"2023_JourGraphAlgorithms_Arroyo.pdf","relation":"main_file","file_id":"13979","content_type":"application/pdf"}],"article_type":"original","status":"public","date_updated":"2023-09-25T10:56:10Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"doi":"10.7155/jgaa.00629","department":[{"_id":"UlWa"}],"oa_version":"Published Version","ec_funded":1,"acknowledgement":"This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1. An extended abstract of this paper has been published in the proceedings of WALCOM 2022 in the Springer LNCS series, vol. 13174, pages 383–395.","file_date_updated":"2023-08-07T08:00:48Z","page":"433-457","author":[{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","full_name":"Arroyo Guevara, Alan M","last_name":"Arroyo Guevara","orcid":"0000-0003-2401-8670","first_name":"Alan M"},{"full_name":"Felsner, Stefan","first_name":"Stefan","last_name":"Felsner"}],"language":[{"iso":"eng"}],"day":"01","year":"2023","oa":1,"abstract":[{"text":"Bundling crossings is a strategy which can enhance the readability\r\nof graph drawings. In this paper we consider good drawings, i.e., we require that\r\nany two edges have at most one common point which can be a common vertex or a\r\ncrossing. Our main result is that there is a polynomial-time algorithm to compute an\r\n8-approximation of the bundled crossing number of a good drawing with no toothed\r\nhole. In general the number of toothed holes has to be added to the 8-approximation.\r\nIn the special case of circular drawings the approximation factor is 8, this improves\r\nupon the 10-approximation of Fink et al. [14]. Our approach also works with the same\r\napproximation factor for families of pseudosegments, i.e., curves intersecting at most\r\nonce. We also show how to compute a 9/2-approximation when the intersection graph of\r\nthe pseudosegments is bipartite and has no toothed hole.","lang":"eng"}],"scopus_import":"1","volume":27,"date_published":"2023-07-01T00:00:00Z","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","publication_identifier":{"issn":["1526-1719"]},"ddc":["510"],"intvolume":"        27","title":"Approximating the bundled crossing number","citation":{"mla":"Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” <i>Journal of Graph Algorithms and Applications</i>, vol. 27, no. 6, Brown University, 2023, pp. 433–57, doi:<a href=\"https://doi.org/10.7155/jgaa.00629\">10.7155/jgaa.00629</a>.","ista":"Arroyo Guevara AM, Felsner S. 2023. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 27(6), 433–457.","ieee":"A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” <i>Journal of Graph Algorithms and Applications</i>, vol. 27, no. 6. Brown University, pp. 433–457, 2023.","apa":"Arroyo Guevara, A. M., &#38; Felsner, S. (2023). Approximating the bundled crossing number. <i>Journal of Graph Algorithms and Applications</i>. Brown University. <a href=\"https://doi.org/10.7155/jgaa.00629\">https://doi.org/10.7155/jgaa.00629</a>","chicago":"Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” <i>Journal of Graph Algorithms and Applications</i>. Brown University, 2023. <a href=\"https://doi.org/10.7155/jgaa.00629\">https://doi.org/10.7155/jgaa.00629</a>.","ama":"Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. <i>Journal of Graph Algorithms and Applications</i>. 2023;27(6):433-457. doi:<a href=\"https://doi.org/10.7155/jgaa.00629\">10.7155/jgaa.00629</a>","short":"A.M. Arroyo Guevara, S. Felsner, Journal of Graph Algorithms and Applications 27 (2023) 433–457."},"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"11185"}]},"article_processing_charge":"Yes"}