Moving vertices to make drawings plane

Authors:
Xavier Goaoc;Jan Kratochvíl;Yoshio Okamoto;Chan-Su Shin;Alexander Wolff
Affiliations:
LORIA, INRIA Lorraine, Nancy, France;Dept. Applied Math. and Inst. Theoret. Comp. Science, Charles Univ., Czech Rep.;Dept. Information and Computer Sciences, Toyohashi Univ. of Technology, Japan;School of Digital Inform. Eng., Hankuk Univ. of Foreign Studies, Yongin, Korea;Faculteit Wiskunde en Informatica, TU Eindhoven, The Netherlands
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

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Abstract

In John Tantalo's on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by moving vertices. In this paper we investigate the related problem MINMOVEDVERTICES which asks for the minimum number of vertex moves. First, we show that MINMOVEDVERTICES is NP-hard and hard to approximate. Second, we establish a connection to the graph-drawing problem 1BENDPOINTSETEMBED- DABILITY, which yields similar results for that problem. Third, we give bounds for the behavior of MINMOVEDVERTICES on trees and general planar graphs.