New algorithms for 1-D facility location and path equipartition problems

Abstract

We study the one-dimensional facility location problems. Given a set of n customers on the real line, each customer having a cost for setting up a facility at its position, and an integer k, we seek to find at most k of the customers to set up facilities for serving all n customers such that the total cost for facility set-up and service transportation is minimized. We consider several problem variations including k-median and k-coverage and a linear model. We also study a related path equipartition problem: Given a vertex-weighted path and an integer k, remove k - 1 edges so that the weights of the resulting k sub-paths are as equal as possible. Based on new problem modeling and observations, we present improved algorithms for these problems over the previous work. © 2011 Springer-Verlag.