{"date_created":"2022-04-17T22:01:47Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","series_title":"LNCS","oa_version":"Preprint","oa":1,"scopus_import":"1","publisher":"Springer Nature","status":"public","related_material":{"record":[{"status":"public","id":"13969","relation":"later_version"}]},"quality_controlled":"1","title":"Approximating the bundled crossing number","day":"16","type":"conference","date_updated":"2023-09-25T10:56:10Z","article_processing_charge":"No","month":"03","publication_status":"published","date_published":"2022-03-16T00:00:00Z","abstract":[{"text":"Bundling crossings is a strategy which can enhance the readability of graph drawings. In this paper we consider bundlings for families of pseudosegments, i.e., simple curves such that any two have share at most one point at which they cross. Our main result is that there is a polynomial-time algorithm to compute an 8-approximation of the bundled crossing number of such instances (up to adding a term depending on the facial structure). This 8-approximation also holds for bundlings of good drawings of graphs. In the special case of circular drawings the approximation factor is 8 (no extra term), this improves upon the 10-approximation of Fink et al. [6]. We also show how to compute a 92-approximation when the intersection graph of the pseudosegments is bipartite.","lang":"eng"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2109.14892","open_access":"1"}],"department":[{"_id":"UlWa"}],"volume":13174,"intvolume":"     13174","year":"2022","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 Sklodowska Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1.","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication":"WALCOM 2022: Algorithms and Computation","author":[{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M","last_name":"Arroyo Guevara"},{"last_name":"Felsner","first_name":"Stefan","full_name":"Felsner, Stefan"}],"page":"383-395","doi":"10.1007/978-3-030-96731-4_31","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030967307"],"issn":["0302-9743"]},"external_id":{"arxiv":["2109.14892"]},"conference":{"end_date":"2022-03-26","location":"Jember, Indonesia","start_date":"2022-03-24","name":"WALCOM: Algorithms and Computation"},"citation":{"ama":"Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. In: <i>WALCOM 2022: Algorithms and Computation</i>. Vol 13174. LNCS. Springer Nature; 2022:383-395. doi:<a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">10.1007/978-3-030-96731-4_31</a>","ista":"Arroyo Guevara AM, Felsner S. 2022. Approximating the bundled crossing number. WALCOM 2022: Algorithms and Computation. WALCOM: Algorithms and ComputationLNCS vol. 13174, 383–395.","apa":"Arroyo Guevara, A. M., &#38; Felsner, S. (2022). Approximating the bundled crossing number. In <i>WALCOM 2022: Algorithms and Computation</i> (Vol. 13174, pp. 383–395). Jember, Indonesia: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">https://doi.org/10.1007/978-3-030-96731-4_31</a>","chicago":"Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” In <i>WALCOM 2022: Algorithms and Computation</i>, 13174:383–95. LNCS. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">https://doi.org/10.1007/978-3-030-96731-4_31</a>.","short":"A.M. Arroyo Guevara, S. Felsner, in:, WALCOM 2022: Algorithms and Computation, Springer Nature, 2022, pp. 383–395.","mla":"Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” <i>WALCOM 2022: Algorithms and Computation</i>, vol. 13174, Springer Nature, 2022, pp. 383–95, doi:<a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">10.1007/978-3-030-96731-4_31</a>.","ieee":"A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” in <i>WALCOM 2022: Algorithms and Computation</i>, Jember, Indonesia, 2022, vol. 13174, pp. 383–395."},"ec_funded":1,"_id":"11185","language":[{"iso":"eng"}]}