A better-than-greedy approximation algorithm for the minimum set cover problem

Refael Hassin, Asaf Levin

Research output: Contribution to journalArticlepeer-review

Abstract

In the weighted set-cover problem we are given a set of elements E = {e1, e2,..., en} and a collection F of subsets of E, where each 5 ∈ F has a positive cost cS. The problem is to compute a subcollection SOL such that US∈SOL Sj = E and = E∈SOL cS is minimized. When |S| ≤ k ∀S ∈ F we obtain the weighted k-set cover problem. It is well known that the greedy algorithm is an Hk-approximation algorithm for the weighted k set cover, where Hk = ∑i=1k 1/i is the kth harmonic number, and that this bound is exact for the greedy algorithm for all constant values of k. In this paper we give the first improvement on this approximation ratio for all constant values of k. This result shows that the greedy algorithm is not the best possible for approximating the weighted set cover problem. Our method is a modification of the greedy algorithm that allows the algorithm to regret.

Original languageEnglish
Pages (from-to)189-200
Number of pages12
JournalSIAM Journal on Computing
Volume35
Issue number1
DOIs
StatePublished - 2006

Keywords

  • Approximation algorithms
  • Greedy algorithm
  • Set cover problem

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