Computational Comparison of Two Lagrangian Relaxation for the K-median Problem

Abstract

The k-median problem has been widely studies both from the theoretical point of view and for its application. An interesting theoretical development was the successful probabilistic analysis of several heuristics (e.g. Fisher and Hochbaum[7], Papadimitriou[12]), relaxations (e.g. Ahn et al [2]), and polyhedral study(Ahn[2], Guignard[9]) for this problem. On the other hand, the literature on the k-median problem abounds in exact algorithms. Most(e.g. Cornuejols et al[4]) are based on the solution of relaxation. The computational experience reported in the literature seems to indicate that this relaxation yields impressively tight bounds compared to what can usually be expected in integer programming. In this paper we perform extensive computational analysis of two Largarangian relaxation for the k-median problem...