Computing the Maximum Detour of a Plane Graph in Subquadratic Time

Abstract

Let G be a plane graph where each edge is a line segment. We consider the problem of computing the maximum detour of G, defined as the maximum over all pairs of distinct points p and q of G of the ratio between the distance between p and q in G and the distance |pq|. The fastest known algorithm for this problem has Θ(n 2) running time where n is the number of vertices. We show how to obtain O(n 3/2log3 n) expected running time. We also show that if G has bounded treewidth, its maximum detour can be computed in O(nlog3 n) expected time.KeywordsShort PathRecursive CallGeometric GraphExpected TimeDual ColourThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.