A parallel algorithm for minimum weight set cover with small neighborhood property
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This paper studies the minimum weight set cover (MinWSC) problem with a small neighborhood cover (SNC) property proposed by Agarwal et al. in <cit.>. A parallel algorithm for MinWSC with τ-SNC property is presented, obtaining approximation ratio τ(1+3ε) in O(Llog_1+εn^3/ε^2+ 4τ^32^τ L^2log n) rounds, where 0< ε <1/2 is a constant, n is the number of elements, and L is a parameter related to SNC property. Our results not only improve the approximation ratio obtained in <cit.>, but also answer two questions proposed in <cit.>.
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