Combinatorial approximation algorithms for the maximum directed cut problem

Eran Halperjn*, Uri Zwick

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

33 Scopus citations

Abstract

We describe several combinatorial algorithms for the maximum directed cut problem. Among our results is a simple linear time 9/20-approximation algorithm for the problem, and a somewhat slower 1/2-approximation algorithm that uses a bipartite matching routine. No better combinatorial approximation algorithms are known even for the easier maximum cut problem for undirected graphs. Our algorithms do not use linear programming, nor semidefinite programming. They are based on the observation that the maximum directed cut problem is equivalent to the problem of finding a maximum independent set in the line graph of the input graph, and that the linear programming relaxation of the problem is equivalent to the problem of finding a maximum fractional independent set of that line graph. The maximum fractional independent set problem can be easily reduced to a bipartite matching problem. As a consequence of this relation, we also get that the maximum directed cut problem for bipartite digraphs can be solved in polynomial time.

Original languageEnglish
Title of host publicationProceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages1-7
Number of pages7
StatePublished - 2001
Event2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States
Duration: 30 Apr 20011 May 2001

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference2001 Operating Section Proceedings, American Gas Association
Country/TerritoryUnited States
CityDallas, TX
Period30/04/011/05/01

Keywords

  • Algorithms
  • Theory
  • Verification

Fingerprint

Dive into the research topics of 'Combinatorial approximation algorithms for the maximum directed cut problem'. Together they form a unique fingerprint.

Cite this