Polyhedral Properties of the K-median Problem on a Tree

Authors:
Sven de Vries;Marc E. Posner;Rakesh V. Vohra
Affiliations:
TU München, Zentrum Mathematik, 85747, Garching bei München, Germany;The Ohio State University, Industrial Engineering, 43210, Columbus, OH, USA;Northwestern University, Department of Managerial Economics and Decision Sciences, The Kellogg School, 60208, Evanston, IL, USA
Venue:
Mathematical Programming: Series A and B
Year:
2007

Citing 0
Cited 2

On the linear relaxation of the p-median problem

Discrete Optimization
On the p-median polytope of Y-free graphs

Discrete Optimization

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Abstract

The polyhedral structure of the K-median problem on a tree is examined. Even for very small connected graphs, we show that additional constraints are needed to describe the integer polytope. A complete description is given of those trees for which an optimal integer LP solution is guaranteed to exist. We present a new and simpler demonstration that an LP characterization of the 2-median problem is complete. Also, we provide a simpler proof of the value of a tight worst case bound for the LP relaxation. A new class of valid inequalities is identified. These inequalities describe a subclass of facets for the K-median problem on a general graph. Also, we provide polyhedral descriptions for several types of trees. As part of this work, we summarize most known results for the K-median problem on a tree.