Computing the Maximum Detour of a Plane Graph in Subquadratic Time

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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 O(n^2) running time. We show how to obtain O(n^{3/2}*(log n)^3) expected running time. We also show that if G has bounded treewidth, its maximum detour can be computed in O(n*(log n)^3) expected time.
Original languageEnglish
Place of PublicationKøbenhavn
PublisherDepartment of Computer Science, University of Copenhagen
Number of pages25
Publication statusPublished - 2008

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