Parallel approximation for partial set cover

Yingli Ran, Ying Zhang and Zhao Zhang

Applied Mathematics and Computation, 2021, vol. 408, issue C

Abstract: In a minimum partial set cover problem (MinPSC), given a ground set E with n elements, a collection S of subsets of E with |S|=m, a cost function c:S→R+, and an integer k≤n, the goal of MinPSC is to find a minimum cost sub-collection of S that covers at least k elements of E. In this paper, we design a parallel algorithm for MinPSC which yields a solution with approximation ratio at most f1−2ε in O(1εlogmnε) rounds, where f is the maximum number of sets containing a common element, and 0<ε<1/2 is a constant. We also design a parallel algorithm for a special MinPSC problem, the minimum power partial cover problem (MinPPC), which achieves approximation ratio at most (3+2ε)α1−2ε in O(1εlogmnεlog2m) rounds, where α≥1 is the attenuation factor of power.

Keywords: Minimum partial set cover; Minimum power partial cover; Parallel algorithm; Approximation ratio (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004471

DOI: 10.1016/j.amc.2021.126358

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