On-line Computation for the Euclidean P-Median Problems

Abstract

The Euclidean p-median problem is to locate p facilities and allocate n fixed demand points each to one and only one of these facilities so that the weighted sum of the distances between the facilities and the demand points is minimal. In the conventional version of this problem, the p facilities are to be located simultaneously. This problem is known to be NP-complete. An online version of this problem requires the solution to be spread over p steps. In each step, a new facility is added and is to be located without relocating the existing facilities whereas some demand points may have to be reallocated. In this paper, it is first shown that a greedy on-line algorithm for this problem has no finite competitive ratio. An on-line algorithm with competitive ratio 2n is then proposed.