Monotone drawings of graphs with fixed embedding

Angelini, P; Didimo, W; Kobourov, S; McHedlidze, T; Roselli, V; Symvonis, A; Wismath, S

dc.contributor.author	Angelini, P	en
dc.contributor.author	Didimo, W	en
dc.contributor.author	Kobourov, S	en
dc.contributor.author	McHedlidze, T	en
dc.contributor.author	Roselli, V	en
dc.contributor.author	Symvonis, A	en
dc.contributor.author	Wismath, S	en
dc.date.accessioned	2014-03-01T02:53:55Z
dc.date.available	2014-03-01T02:53:55Z
dc.date.issued	2012	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/36487
dc.subject.other	A-monotone	en
dc.subject.other	Drawing algorithms	en
dc.subject.other	Linear time	en
dc.subject.other	Planar graph	en
dc.subject.other	Drawing (graphics)	en
dc.subject.other	Graph theory	en
dc.title	Monotone drawings of graphs with fixed embedding	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-25878-7_36	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-25878-7_36	en
heal.publicationDate	2012	en
heal.abstract	A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n - 10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time. © 2012 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	10.1007/978-3-642-25878-7_36	en
dc.identifier.volume	7034 LNCS	en
dc.identifier.spage	379	en
dc.identifier.epage	390	en