Minimum weight pseudo-triangulations (extended abstract)

Abstract

We consider the problem of computing a minimum weight pseudo-triangulation of a set S of n points in the plane. We first present an script O sign(n log n)-time algorithm that produces a pseudo-triangulation of weight script O sign(wt(script M sign(S)) · log n) which is shown to be asymptotically worst-case optimal, i.e., there exists a point set S for which every pseudo-triangulation has weight Ω(log n · wt(script M sign(S))), where wt(script M sign(S)) is the weight of a minimum spanning tree of S. We also present a constant factor approximation algorithm running in cubic time. In the process we give an algorithm that produces a minimum weight pseudo-triangulation of a simple polygon. © Springer-Verlag Berlin Heidelberg 2004.