ISAAC 2008: Algorithms and Computation pp 740-751

# Computing the Maximum Detour of a Plane Graph in Subquadratic Time

• Christian Wulff-Nilsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

## 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.

## Keywords

Short Path Recursive Call Geometric Graph Expected Time Dual Colour
These 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.

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