Many Distances in Planar Graphs

Authors:
Sergio Cabello
Affiliations:
University of Ljubljana, Department of Mathematics, Faculty of Mathematics and Physics, Ljubljana, Slovenia and Institute for Mathematics, Physics and Mechanics, Department of Mathematics, Ljublja ...
Venue:
Algorithmica
Year:
2012

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Cited 4

Improved distance queries in planar graphs

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Abstract

We show how to compute in O(n 4/3log 1/3 n+n 2/3 k 2/3log n) time the distance between k given pairs of vertices of a planar graph G with n vertices. This improves previous results whenever (n/log n)5/6≤k≤n 2/log 6 n. As an application, we speed up previous algorithms for computing the dilation of geometric planar graphs.