Lecture Notes in Computer Science Volume 3843, 2006, pp 13-24

Morphing Planar Graphs While Preserving Edge Directions

Purchase on Springer.com

$29.95 / €24.95 / £19.95*

* Final gross prices may vary according to local VAT.

Get Access

Abstract

Two straight-line drawings P,Q of a graph (V,E) are called parallel if, for every edge (u,v) ∈ E, the vector from u to v has the same direction in both P and Q. We study problems of the form: given simple, parallel drawings P,Q does there exist a continuous transformation between them such that intermediate drawings of the transformation remain simple and parallel with P (and Q)? We prove that a transformation can always be found in the case of orthogonal drawings; however, when edges are allowed to be in one of three or more slopes the problem becomes NP-hard.