Minimum power partial multi-cover on a line

Abstract

This paper studies the minimum power partial multi-cover problem on a line (MinPowPMC-Line), the goal of which is to find an assignment of powers to sensors such that at least a required number of points are covered up to their covering requirements. We first present an LP method to show that the minimum power multi-cover problem on a line (without partial covering requirement) is solvable in polynomial time. But this method no longer works when facing partial covering requirement. We turn to dynamic programming method to find an optimal solution for MinPowPMC-Line in time O(n4m1+2(crmax)), where n,m are the number of points and the number of sensors, respectively, and crmax denotes the maximum covering requirement of elements. So, this problem is polynomial-time solvable when crmax is upper bounded by a constant.