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 O(nlogn) -time algorithm that produces a pseudo-triangulation of weight O(wt(M(S)).logn) which is shown to be asymptotically worst-case optimal, i.e., there exists a point set S for which every pseudo-triangulation has weight O(logn.wt(M(S)) , where wt(M(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.
|Title of host publication||Foundations of Software Technology and Theoretical Computer Science (Proceedings 24th Conference, FSTTCS 2004, Chennai, India, December 16-18, 2004)|
|Editors||K. Lodaya, M. Mahajan|
|Place of Publication||Berlin|
|Publication status||Published - 2004|
|Name||Lecture Notes in Computer Science|