An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty

Abstract

In this paper, we consider the minimum power cover problem with submodular penalty (SPMPC). Given a set U of n users, a set S of m sensors and a penalty function π:2U→R+ on the plane, the relationship that adjusts the power p(s) of each sensor s and its corresponding radius r(s) is: p(s)=c·r(s)α, where c>0 and α≥1. The SPMPC problem is to determine the power assignment on each sensor such that each user u∈U is either covered by the sensor or penalized and the sum of the total power consumed by sensors in S plus the penalty of all uncovered users is minimized, the penalty here is determined by the submodular function. Based on the primal dual technique, we design an O(α)-approximation algorithm.