A parallel algorithm for minimum weight set cover with small neighborhood property

Abstract

This paper studies the minimum weight set cover (MinWSC) problem with a small neighborhood cover property (τ-SNC). A parallel algorithm is presented, obtaining approximation ratio $\tau (1+3\epsilon )$ in $O(L{\log }_{1+\epsilon }\frac{n^3}{{\epsilon }^2}+4{\tau }^3{2}^{\tau }{L}^2\log n)$ rounds, where $0<\epsilon <\frac{1}{2}$ is a constant, n is the number of elements, and L is the depth of SNC-decomposition. Our results not only improve the approximation ratio obtained in [2], but also answer two questions proposed in [2].