A shortest cycle for each vertex of a graph

Authors:
Raphael Yuster
Affiliations:
Department of Mathematics, University of Haifa, Haifa 31905, Israel
Venue:
Information Processing Letters
Year:
2011

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Abstract

We present an algorithm that finds, for each vertex of an undirected graph, a shortest cycle containing it. While for directed graphs this problem reduces to the All-Pairs Shortest Paths problem, this is not known to be the case for undirected graphs. We present a truly sub-cubic randomized algorithm for the undirected case. Given an undirected graph with n vertices and integer weights in 1,...,M, it runs in O@?(Mn^(^@w^+^3^)^/^2) time where @w