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The Demand Matching Problem

  • Bruce Shepherd
  • Adrian Vetta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2337)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Bruce Shepherd
    • 1
  • Adrian Vetta
    • 2
  1. 1.Bell LaboratoriesUSA
  2. 2.Massachusetts Institute of TechnologyUSA

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