Two polynomial time algorithms for the metro-line crossing minimization problem

Argyriou, E; Bekos, MA; Kaufmann, M; Symvonis, A

dc.contributor.author	Argyriou, E	en
dc.contributor.author	Bekos, MA	en
dc.contributor.author	Kaufmann, M	en
dc.contributor.author	Symvonis, A	en
dc.date.accessioned	2014-03-01T02:52:13Z
dc.date.available	2014-03-01T02:52:13Z
dc.date.issued	2009	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35873
dc.subject.other	Embedded graphs	en
dc.subject.other	IMPROVE-A	en
dc.subject.other	Line crossings	en
dc.subject.other	Main tasks	en
dc.subject.other	Metro maps	en
dc.subject.other	Polynomial-time algorithms	en
dc.subject.other	Public transportation networks	en
dc.subject.other	Crossings (pipe and cable)	en
dc.subject.other	Drawing (graphics)	en
dc.subject.other	Polynomial approximation	en
dc.subject.other	Graph theory	en
dc.title	Two polynomial time algorithms for the metro-line crossing minimization problem	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-00219-9-33	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-00219-9-33	en
heal.publicationDate	2009	en
heal.abstract	The metro-line crossing minimization (MLCM) problem was recently introduced as a response to the problem of drawing metro maps or public transportation networks, in general. According to this problem, we are given a planar, embedded graph G∈=∈(V,E) and a set L of simple paths on G, called lines. The main task is to place the lines on G, so that the number of crossings among pairs of lines is minimized. Our main contribution is two polynomial time algorithms. The first solves the general case of the MLCM problem, where the lines that traverse a particular vertex of G are allowed to use any side of it to either ""enter"" or ""exit"", assuming that the endpoints of the lines are located at vertices of degree one. The second one solves more efficiently the restricted case, where only the left and the right side of each vertex can be used. To the best of our knowledge, this is the first time where the general case of the MLCM problem is solved. Previous work was devoted to the restricted case of the MLCM problem under the additional assumption that the endpoints of the lines are either the topmost or the bottommost in their corresponding vertices, i.e., they are either on top or below the lines that pass through the vertex. Even for this case, we improve a known result of Asquith et al. from O(\|E\|5/2\|L\|3) to O(\|V\|(\|E\|∈ +∈\|L\|)). © 2009 Springer Berlin Heidelberg.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-642-00219-9-33	en
dc.identifier.volume	5417 LNCS	en
dc.identifier.spage	336	en
dc.identifier.epage	347	en