On the p-Median Polytope of a Special Class of Graphs

In this paper we consider a well known class of valid inequalities for the p-median and the uncapacitated facility location polytopes, the odd cycle inequalities. It is known that their separation problem is polynomially solvable. We give a new polynomial separation algorithm based on a reduction from the original graph. Then, we define a nontrivial class of graphs, where the odd cycle inequalities together with the linear relaxations of both the p-median and uncapacitated facility location problems, suffice to describe the associated polytope. To do this, we rst give a complete description of the fractional extreme points of the linear relaxation for the p-median polytope in that class of graphs.

By: Mourad Baïou; Francisco Barahona

Published in: RC23636 in 2005


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