An improved algorithm for the p-center problem on interval graphs with unit lengths

The p-center problem is to locate p facilities in a network of n   demand points so as to minimize the longest distance between a demand point and its nearest facility. We consider this problem by modelling the network as an interval graph whose edges all have unit lengths. We present an O(n)O(n) time algorithm for the problem under the assumption that the endpoints of the intervals are sorted, which improves on the existing best algorithm for the problem that has a run time of O(pn)O(pn).