Randomized Approximation of Bounded Multicovering Problems

D. Peleg, G. Schechtman, A. Wool

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of finding approximate solutions for a subclass of multicovering problems denoted by ILP(k, b) is considered. The problem involves finding x ∈ {0, 1}n that minimizes ∑jxj subject to the constraint Ax ≥ b, where A is a 0-1 m × n matrix with at most k ones per row, b is an integer vector, and b is the smallest entry in b. This subclass includes, for example, the Bounded Set Cover problem when b = 1, and the Vertex Cover problem when k = 2 and b=1. An approximation ratio of k - b + 1 is achievable by known deterministic algorithms. A new randomized approximation algorithm is presented, with an approximation ratio of (k - b + 1)(1 - (c/m)1/(k - b + 1)) for a small constant c > 0. The analysis of this algorithm relies on the use of a new bound on the sum of independent Bernoulli random variables, that is of interest in its own right.

Original languageEnglish
Pages (from-to)44-66
Number of pages23
JournalAlgorithmica
Volume18
Issue number1
DOIs
StatePublished - May 1997
Externally publishedYes

Keywords

  • Approximation algorithms
  • Integer linear programs
  • Randomized rounding
  • Set cover

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