Moving vertices to make drawings plane

Xavier Goaoc (1) , Jan Kratochvil (2) , Yoshio Okamoto (3) , Chan-Su Shin (4) , Alexander Wolff (5)

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
2 KAM - Department of Applied Mathematics (KAM)
3 Discrete Optimization Laboratory
4 Departement of Electronics and Information Engineering
5 Faculteit Wiskunde & Informatica

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 1BendPointSetEmbeddability, which yields similar results for that problem. Third, we give bounds for the behavior of MinMovedVertices on trees and general planar graphs.

Domaines: Géométrie algorithmique [cs.CG]

Xavier Goaoc, Jan Kratochvil, Yoshio Okamoto, Chan-Su Shin, Alexander Wolff. Moving vertices to make drawings plane. 15th International Symposium on Graph Drawing, Sep 2007, Sydney, Australia. pp.101-112, ⟨10.1007/978-3-540-77537-9_13⟩. ⟨inria-00181775⟩