A modified greedy algorithm for dispersively weighted 3-set cover

  • Authors:

  • Toshihiro Fujito;Tsuyoshi Okumura

  • Affiliations:

  • Department of Information and Computer Sciences, Toyohashi University of Technology, Hibarigaoka, Tempaku, Toyohashi 441-8580, Japan;Department of Information Electronics, Nagoya University, Furo, Chikusa, Nagoya 464-8603, Japan

  • Venue:
  • Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

The set cover problem is that of computing a minimum weight subfamily F^', given a family F of weighted subsets of a base set U, such that every element of U is covered by some subset in F^'. The k-set cover problem is a variant in which every subset is of size at most k. It has been long known that the problem can be approximated within a factor of H(k)=@?"i"="1^k(1/i) by the greedy heuristic, but no better bound has been shown except for the case of unweighted subsets. In this paper we consider approximation of a restricted version of the weighted 3-set cover problem, as a first step towards better approximation of general k-set cover problem, where any two distinct subset costs differ by a multiplicative factor of at least 2. It will be shown, via LP duality, that an improved approximation bound of H(3)-1/6 can be attained, when the greedy heuristic is suitably modified for this case. A key to our algorithm design and analysis is the Gallai-Edmonds structure theorem for maximum matchings.