On the complexity of approximating k-dimensional matching

Elad Hazan, Shmuel Safra, Oded Schwartz

Research output: Chapter in Book/Report/Conference proceedingChapter

40 Scopus citations

Abstract

We study the complexity of bounded variants of graph problems, mainly the problem of k-Dimensional Matching (k-DM), namely, the problem of finding a maximal matching in a k-partite k-uniform balanced hyper-graph. We prove that k-DM cannot be efficiently approximated to within a factor of O(k/ln k) unless P = NP. This improves the previous factor of k/2O(√ln k) by Trevisan [Tre01]. For low k values we prove NP-hardness factors of 54/53-ε, 30/29-ε and 23/22-ε for 4-DM, 5-DM and 6-DM respectively. These results extend to the problem of k-Set-Packing and the problem of Maximum Independent-Set in (k + 1)-claw-free graphs.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsSanjeev Asora, Amit Sahai, Klaus Jansen, Jose D.P. Rolim
PublisherSpringer Verlag
Pages83-97
Number of pages15
ISBN (Print)3540407707, 9783540407706
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2764
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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