Line crossing minimization on metro maps

Bekos, MA; Kaufmann, M; Potika, K; Symvonis, A

dc.contributor.author	Bekos, MA	en
dc.contributor.author	Kaufmann, M	en
dc.contributor.author	Potika, K	en
dc.contributor.author	Symvonis, A	en
dc.date.accessioned	2014-03-01T02:51:44Z
dc.date.available	2014-03-01T02:51:44Z
dc.date.issued	2008	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35615
dc.subject	Crossing minimization	en
dc.subject	Lines	en
dc.subject	Metro maps	en
dc.subject	Paths	en
dc.subject	Trees	en
dc.subject.other	Crossings (pipe and cable)	en
dc.subject.other	Drawing (graphics)	en
dc.subject.other	Graph theory	en
dc.subject.other	Maps	en
dc.subject.other	Optical projectors	en
dc.subject.other	Arbitrary graphs	en
dc.subject.other	Crossing minimization	en
dc.subject.other	Crossing minimization problem	en
dc.subject.other	Graph drawing	en
dc.subject.other	Graph G	en
dc.subject.other	International symposium	en
dc.subject.other	Lines	en
dc.subject.other	Metro maps	en
dc.subject.other	Optimal solutions	en
dc.subject.other	Paths	en
dc.subject.other	Railway lines	en
dc.subject.other	Terminal stations	en
dc.subject.other	Train stations	en
dc.subject.other	Tree networks	en
dc.subject.other	Trees	en
dc.subject.other	Variations of	en
dc.subject.other	Trees (mathematics)	en
dc.title	Line crossing minimization on metro maps	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-540-77537-9_24	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-540-77537-9_24	en
heal.publicationDate	2008	en
heal.abstract	We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G∈=∈(V,E), so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying network, the nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway line which connects them, whereas the paths illustrate the lines connecting terminal stations. We call this the metro-line crossing minimization problem (MLCM). In contrast to the problem of drawing the underlying graph nicely, MLCM has received fewer attention. It was recently introduced by Benkert et. al in [4] . In this paper, as a first step towards solving MLCM in arbitrary graphs, we study path and tree networks. We examine several variations of the problem for which we develop algorithms for obtaining optimal solutions. © 2008 Springer-Verlag 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	10.1007/978-3-540-77537-9_24	en
dc.identifier.volume	4875 LNCS	en
dc.identifier.spage	231	en
dc.identifier.epage	242	en