An improved approximation algorithm for vertex cover with hard capacities (extended abstract)

Rajiv Gandhi, Eran Halperin, Samir Khuller, Guy Kortsarz, Aravind Srinivasan

Research output: Chapter in Book/Report/Conference proceedingChapter

17 Scopus citations

Abstract

In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V, E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. Previously, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481-489, 2002) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsJos C. M. Baeten, Jan Karel Lenstra, Joachim Parrow, Gerhard J. Woeginger
PublisherSpringer Verlag
Pages164-175
Number of pages12
ISBN (Print)3540404937, 9783540404934
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2719
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Keywords

  • Approximation algorithms
  • Capacitated covering
  • Linear programming
  • Randomized rounding
  • Set cover
  • Vertex cover

Fingerprint

Dive into the research topics of 'An improved approximation algorithm for vertex cover with hard capacities (extended abstract)'. Together they form a unique fingerprint.

Cite this