An approximation algorithm for MAX DICUT with given sizes of parts

Alexander Ageev, Refael Hassin, Maxim Sviridenko

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

1 Scopus citations

Abstract

Given a directed graph G and an edge weight function w: E(G) → ℝ+, the maximum directed cut problem (MAX DICUT) is that of finding a directed cut δ(X) with maximum total weight. In this paper we consider a version of MAX DICUT — MAX DICUT with given sizes of parts or MAX DICUT WITH GSP — whose instance is that of MAX DICUT plus a positive integer p, and it is required to find a directed cut δ(X) having maximum weight over all cuts δ(X) with |X| = p. It is known that by using semidefinite programming rounding techniques MAX DICUT can be well approximated — the best approximation with a factor of 0.859 is due to Feige and Goemans. Unfortunately, no similar approach is known to be applicable to max DICUT WITH GSP. This paper presents an 0.5- approximation algorithm for solving the problem. The algorithm is based on exploiting structural properties of basic solutions to a linear relaxation in combination with the pipage rounding technique developed in some earlier papers by two of the authors.

Original languageEnglish
Title of host publicationApproximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings
EditorsKlaus Jansen, Samir Khuller
PublisherSpringer Verlag
Pages34-41
Number of pages8
ISBN (Electronic)9783540679967
DOIs
StatePublished - 2000
Event3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, Germany
Duration: 5 Sep 20008 Sep 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1913
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000
Country/TerritoryGermany
CitySaarbrucken
Period5/09/008/09/00

Funding

FundersFunder number
Russian Foundation for Basic Research99-01-00601, 99-01-00510

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