[{"arxiv":1,"quality_controlled":"1","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07608"}],"abstract":[{"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.","lang":"eng"}],"date_created":"2018-12-30T22:59:15Z","oa":1,"type":"conference","month":"12","title":"Crossing minimization in perturbed drawings","year":"2018","doi":"10.1007/978-3-030-04414-5_16","author":[{"first_name":"Radoslav","last_name":"Fulek","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav"},{"last_name":"Tóth","first_name":"Csaba D.","full_name":"Tóth, Csaba D."}],"page":"229-241","scopus_import":"1","day":"18","publisher":"Springer","publication_status":"published","oa_version":"Preprint","date_published":"2018-12-18T00:00:00Z","volume":"11282 ","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"conference":{"start_date":"2018-09-26","location":"Barcelona, Spain","name":"GD: Graph Drawing and Network Visualization","end_date":"2018-09-28"},"alternative_title":["LNCS"],"article_processing_charge":"No","date_updated":"2025-07-10T11:53:00Z","_id":"5791","external_id":{"isi":["000672802500016"],"arxiv":["1808.07608"]},"department":[{"_id":"UlWa"}],"citation":{"ieee":"R. Fulek and C. D. Tóth, “Crossing minimization in perturbed drawings,” presented at the GD: Graph Drawing and Network Visualization, Barcelona, Spain, 2018, vol. 11282, pp. 229–241.","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>.","ista":"Fulek R, Tóth CD. 2018. Crossing minimization in perturbed drawings. GD: Graph Drawing and Network Visualization, LNCS, vol. 11282, 229–241.","short":"R. Fulek, C.D. Tóth, in:, Springer, 2018, pp. 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>.","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>","apa":"Fulek, R., &#38; Tóth, C. D. (2018). Crossing minimization in perturbed drawings (Vol. 11282, pp. 229–241). Presented at the GD: 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>"},"publication_identifier":{"isbn":["9783030044138"]},"language":[{"iso":"eng"}]}]