Improved approximation algorithms for the partial vertex cover problem

Eran Halperin, Aravind Srinivasan

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

29 Scopus citations

Abstract

The partial vertex cover problemis a generalization of the vertex cover problem: given an undirected graph G = (V,E) and an integer k, we wish to choose a minimum number of vertices such that at least k edges are covered. Just as for vertex cover, 2-approximation algorithms are known for this problem, and it is of interest to see if we can do better than this. The current-best approximation ratio for partial vertex cover, when parameterized by the maximum degree d of G, is (2−Θ(1/d)). We improve on this by presenting a (formula presented)-approximation algorithm for partial vertex cover using semidefinite programming, matching the current-best bound for vertex cover. Our algorithmuses a new rounding technique, which involves a delicate probabilistic analysis.

Original languageEnglish
Title of host publicationApproximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings
EditorsKlaus Jansen, Stefano Leonardi, Vijay Vazirani
PublisherSpringer Verlag
Pages161-174
Number of pages14
ISBN (Print)3540441867, 9783540441861
DOIs
StatePublished - 2002
Externally publishedYes
Event5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002 - Rome, Italy
Duration: 17 Sep 200221 Sep 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2462
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002
Country/TerritoryItaly
CityRome
Period17/09/0221/09/02

Funding

FundersFunder number
Defense Advanced Research Projects AgencyF30602-00-2-0601
National Science FoundationCCR-9820951, CCR-0121555, CCR-0208005

    Keywords

    • Approximation algorithms
    • Partial vertex cover
    • Randomized rounding
    • Semidefinite programming

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