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Approximating Maximum Stable Set and Minimum Graph Coloring Problems with the Positive Semidefinite Relaxation

  • S. J. Benson
  • Y. Ye
Part of the Applied Optimization book series (APOP, volume 50)

Abstract

We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in most graphs and the structure inherent in the problem formulation. Prom the solution to the relaxation, we apply a randomized algorithm to find approximate maximum stable sets and a modification of a popular heuristic to find graph colorings. We obtained high quality answers for graphs with over 1000 vertices and over 6000 edges.

Keywords

Stable Set Independent Set Maximum Clique Graph Coloring Positive Semidefinite Relaxation 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • S. J. Benson
    • 1
  • Y. Ye
    • 2
  1. 1.Division of Mathematics and Computer ScienceArgonne National LaboratoryArgonneUSA
  2. 2.Department of Management SciencesThe University of IowaIowa CityUSA

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