{"title":"Crossing minimization in perturbed drawings","_id":"5791","department":[{"_id":"UlWa"}],"date_created":"2018-12-30T22:59:15Z","date_updated":"2023-09-11T12:49:55Z","page":"229-241","month":"12","volume":"11282 ","year":"2018","type":"conference","author":[{"orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","first_name":"Radoslav","full_name":"Fulek, Radoslav","last_name":"Fulek"},{"full_name":"Tóth, Csaba D.","last_name":"Tóth","first_name":"Csaba D."}],"isi":1,"oa_version":"Preprint","oa":1,"publication_status":"published","quality_controlled":"1","external_id":{"isi":["000672802500016"],"arxiv":["1808.07608"]},"alternative_title":["LNCS"],"day":"18","status":"public","publication_identifier":{"isbn":["9783030044138"]},"date_published":"2018-12-18T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1808.07608","open_access":"1"}],"doi":"10.1007/978-3-030-04414-5_16","scopus_import":"1","conference":{"start_date":"2018-09-26","name":"Graph Drawing and Network Visualization","end_date":"2018-09-28","location":"Barcelona, Spain"},"citation":{"short":"R. Fulek, C.D. Tóth, in:, Springer, 2018, pp. 229–241.","apa":"Fulek, R., &#38; Tóth, C. D. (2018). Crossing minimization in perturbed drawings (Vol. 11282, pp. 229–241). Presented at the Graph Drawing and Network Visualization, Barcelona, Spain: Springer. <a href=\"https://doi.org/10.1007/978-3-030-04414-5_16\">https://doi.org/10.1007/978-3-030-04414-5_16</a>","ista":"Fulek R, Tóth CD. 2018. Crossing minimization in perturbed drawings. Graph Drawing and Network Visualization, LNCS, vol. 11282, 229–241.","mla":"Fulek, Radoslav, and Csaba D. Tóth. <i>Crossing Minimization in Perturbed Drawings</i>. Vol. 11282, Springer, 2018, pp. 229–41, doi:<a href=\"https://doi.org/10.1007/978-3-030-04414-5_16\">10.1007/978-3-030-04414-5_16</a>.","chicago":"Fulek, Radoslav, and Csaba D. Tóth. “Crossing Minimization in Perturbed Drawings,” 11282:229–41. Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-030-04414-5_16\">https://doi.org/10.1007/978-3-030-04414-5_16</a>.","ieee":"R. Fulek and C. D. Tóth, “Crossing minimization in perturbed drawings,” presented at the Graph Drawing and Network Visualization, Barcelona, Spain, 2018, vol. 11282, pp. 229–241.","ama":"Fulek R, Tóth CD. Crossing minimization in perturbed drawings. In: Vol 11282. Springer; 2018:229-241. doi:<a href=\"https://doi.org/10.1007/978-3-030-04414-5_16\">10.1007/978-3-030-04414-5_16</a>"},"abstract":[{"lang":"eng","text":"Due to data compression or low resolution, nearby vertices and edges of a graph drawing may be bundled to a common node or arc. We model such a “compromised” drawing by a piecewise linear map φ:G → ℝ. We wish to perturb φ by an arbitrarily small ε>0 into a proper drawing (in which the vertices are distinct points, any two edges intersect in finitely many points, and no three edges have a common interior point) that minimizes the number of crossings. An ε-perturbation, for every ε>0, is given by a piecewise linear map (Formula Presented), where with ||·|| is the uniform norm (i.e., sup norm). We present a polynomial-time solution for this optimization problem when G is a cycle and the map φ has no spurs (i.e., no two adjacent edges are mapped to overlapping arcs). We also show that the problem becomes NP-complete (i) when G is an arbitrary graph and φ has no spurs, and (ii) when φ may have spurs and G is a cycle or a union of disjoint paths."}],"publisher":"Springer","article_processing_charge":"No","language":[{"iso":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"}