# The Demand Matching Problem

Conference paper

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## Abstract

We examine formulations for the well-known *b*-matching problem in the presence of integer demands on the edges. A subset *M* of edges is feasible if for each node *v*, the total demand of edges in *M* incident to it is at most *b* _{v}. We examine the system of star inequalities for this problem. This system yields an exact linear description for *b*-matchings in bipartite graphs. For the demand version, we show that the integrality gap for this system is at least 2 1/2 and at most 2 13/16. For general graphs, the gap lies between 3 and 3 5/16. A fully polynomial approximation scheme is also presented for the problem on a tree, thus generalizing a well-known result for the knapsack problem.

## Keywords

Bipartite Graph Knapsack Problem Approximation Guarantee Fractional Edge Node Constraint
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© Springer-Verlag Berlin Heidelberg 2002