Affiliation:
1. Department of Mathematics, FMF, University of Ljubljana, Slovenia and Department of Mathematics, IMFM, Slovenia
Abstract
In this article, we show how to compute for
n
-vertex planar graphs in
O
(
n
11/6
polylog(
n
)) expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In
O
(
n
15/8
polylog(
n
)) expected time, we can also compute the number of pairs of vertices at distances smaller than a given threshold. These are the first algorithms for these problems using time
O
(
n
c
) for some constant
c
< 2, even when restricted to undirected, unweighted planar graphs.
Funder
Slovenian Research Agency
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
23 articles.
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