{"status":"public","quality_controlled":"1","title":"Inserting one edge into a simple drawing is hard","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2022-08-28T22:02:01Z","oa":1,"oa_version":"Published Version","scopus_import":"1","publisher":"Springer Nature","publication_status":"published","date_published":"2023-04-01T00:00:00Z","abstract":[{"text":"A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.","lang":"eng"}],"department":[{"_id":"UlWa"}],"day":"01","file":[{"relation":"main_file","checksum":"def7ae3b28d9fd6aec16450e40090302","content_type":"application/pdf","file_name":"2022_DiscreteandComputionalGeometry_Arroyo.pdf","creator":"alisjak","access_level":"open_access","date_updated":"2022-08-29T11:23:15Z","file_id":"12006","success":1,"file_size":1002218,"date_created":"2022-08-29T11:23:15Z"}],"type":"journal_article","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"},"date_updated":"2023-08-14T12:51:25Z","month":"04","article_processing_charge":"Yes (in subscription journal)","file_date_updated":"2022-08-29T11:23:15Z","acknowledgement":"This work was started during the 6th Austrian–Japanese–Mexican–Spanish Workshop on Discrete Geometry in June 2019 in Austria. We thank all the participants for the good atmosphere as well as discussions on the topic. Also, we thank Jan Kynčl for sending us remarks on a preliminary version of this work and an anonymous referee for further helpful comments.Alan Arroyo was funded by the Marie Skłodowska-Curie grant agreement No 754411. Fabian Klute was partially supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 612.001.651 and by the Austrian Science Fund (FWF): J-4510. Irene Parada and Birgit Vogtenhuber were partially supported by the Austrian Science Fund (FWF): W1230 and within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. Irene Parada was also partially supported by the Independent Research Fund Denmark grant 2020-2023 (9131-00044B) Dynamic Network Analysis and by the Margarita Salas Fellowship funded by the Ministry of Universities of Spain and the European Union (NextGenerationEU). Tilo Wiedera was supported by the German Research Foundation (DFG) grant CH 897/2-2.","isi":1,"ddc":["510"],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"volume":69,"intvolume":"        69","year":"2023","ec_funded":1,"citation":{"ama":"Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. Inserting one edge into a simple drawing is hard. <i>Discrete and Computational Geometry</i>. 2023;69:745–770. doi:<a href=\"https://doi.org/10.1007/s00454-022-00394-9\">10.1007/s00454-022-00394-9</a>","ista":"Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. 2023. Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. 69, 745–770.","apa":"Arroyo Guevara, A. M., Klute, F., Parada, I., Vogtenhuber, B., Seidel, R., &#38; Wiedera, T. (2023). Inserting one edge into a simple drawing is hard. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00394-9\">https://doi.org/10.1007/s00454-022-00394-9</a>","chicago":"Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Birgit Vogtenhuber, Raimund Seidel, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is Hard.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00394-9\">https://doi.org/10.1007/s00454-022-00394-9</a>.","short":"A.M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, T. Wiedera, Discrete and Computational Geometry 69 (2023) 745–770.","mla":"Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is Hard.” <i>Discrete and Computational Geometry</i>, vol. 69, Springer Nature, 2023, pp. 745–770, doi:<a href=\"https://doi.org/10.1007/s00454-022-00394-9\">10.1007/s00454-022-00394-9</a>.","ieee":"A. M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, and T. Wiedera, “Inserting one edge into a simple drawing is hard,” <i>Discrete and Computational Geometry</i>, vol. 69. Springer Nature, pp. 745–770, 2023."},"article_type":"original","language":[{"iso":"eng"}],"_id":"11999","page":"745–770","doi":"10.1007/s00454-022-00394-9","publication":"Discrete and Computational Geometry","has_accepted_license":"1","author":[{"orcid":"0000-0003-2401-8670","first_name":"Alan M","last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","full_name":"Arroyo Guevara, Alan M"},{"last_name":"Klute","first_name":"Fabian","full_name":"Klute, Fabian"},{"last_name":"Parada","first_name":"Irene","full_name":"Parada, Irene"},{"full_name":"Vogtenhuber, Birgit","first_name":"Birgit","last_name":"Vogtenhuber"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"full_name":"Wiedera, Tilo","last_name":"Wiedera","first_name":"Tilo"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"external_id":{"isi":["000840292800001"],"arxiv":["1909.07347"]}}