Abstract
The problem of finding approximate solutions for a subclass of multicovering problems denoted byILP(k, b) is considered. The problem involves findingx∈{0,1}n that minimizes ∑ j x j subject to the constraintAx≥b, whereA is a 0–1m×n matrix with at mostk ones per row,b is an integer vector, andb is the smallest entry inb. This subclass includes, for example, the Bounded Set Cover problem whenb=1, and the Vertex Cover problem whenk=2 andb=1.
An approximation ratio ofk−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 constantc>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.
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Communicated by M. X. Goemans.
The first author was supported in part by a Walter and Elise Haas Career Development Award and by a grant from the Israeli Science Foundation. This work was done white the third author was at the Department of Applied Mathematics and Computer Science, The Weizmann Institute, Rehovot 76100, Israel.
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Peleg, D., Schechtman, G. & Wool, A. Randomized approximation of bounded multicovering problems. Algorithmica 18, 44–66 (1997). https://doi.org/10.1007/BF02523687
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DOI: https://doi.org/10.1007/BF02523687