On the P-coverage Problem on the Real Line

Abstract

Abstract: In this paper we consider the p-coverage problem on the real line. We first give a detailed description of an algorithm to solve the coverage problem without the upper bound p on the number of open facilities. Then we analyze how the structure of the optimal solution changes if the setup costs of the facilities are all decreased by the same amount. This result is used to develop a parametric approach to the p-coverage problem which runs in O(pnlogn) time, n being the number of clients. OR/MS subject classification: Analysis of algorithms, computational complexity: parametric application of dynamic programming; Dynamic programming/optimal control, applications: parametric approach to p-coverage problem on the real line; Facilities/equipment planning, location, discrete: p-coverage problem on the real line.