Improved algorithms for detecting negative cost cycles in undirected graphs

Xiaofeng Gu, Kamesh Madduri, K. Subramani, Hong Jian Lai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In this paper, we explore the design of algorithms for the problem of checking whether an undirected graph contains a negative cost cycle (UNCCD). It is known that this problem is significantly harder than the corresponding problem in directed graphs. Current approaches for solving this problem involve reducing it to either the b-matching problem or the T-join problem. The latter approach is more efficient in that it runs in O(n 3) time on a graph with n vertices and m edges, while the former runs in O(n 6) time. This paper shows that instances of the UNCCD problem, in which edge weights are restricted to be in the range {-K••K} can be solved in O(n 2.75•logn) time. Our algorithm is basically a variation of the T-join approach, which exploits the existence of extremely efficient shortest path algorithms in graphs with integral positive weights. We also provide an implementation profile of the algorithms discussed.

Original languageEnglish (US)
Title of host publicationFrontiers in Algorithmics - Third International Workshop, FAW 2009, Proceedings
Pages40-50
Number of pages11
DOIs
StatePublished - Nov 9 2009
Event3rd International Frontiers of Algorithmics Workshop, FAW 2009 - Hefei, China
Duration: Jun 20 2009Jun 23 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5598 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Frontiers of Algorithmics Workshop, FAW 2009
CountryChina
CityHefei
Period6/20/096/23/09

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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