Reoptimization of Weighted Graph and Covering Problems

  • Davide Bilò
  • Peter Widmayer
  • Anna Zych
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5426)

Abstract

Given an instance of an optimization problem and a good solution of that instance, the reoptimization is a concept of analyzing how does the solution change when the instance is locally modified. We investigate reoptimization of the following problems: Maximum Weighted Independent Set, Maximum Weighted Clique, Minimum Weighted Dominating Set, Minimum Weighted Set Cover and Minimum Weighted Vertex Cover. The local modifications we consider are addition or removal of a constant number of edges to the graph, or elements to the covering sets in case of Set Cover problem. We present the following results:
  1. 1

    We provide a PTAS for reoptimization of the unweighted versions of the aforementioned problems when the input solution is optimal.

     
  2. 1

    We provide two general techniques for analyzing approximation ratio of the weighted reoptimization problems.

     
  3. 1

    We apply our techniques to reoptimization of the considered optimization problems and obtain tight approximation ratios in all the cases.

     

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Davide Bilò
    • 1
  • Peter Widmayer
    • 1
  • Anna Zych
    • 1
  1. 1.Institut für Theoretische InformatikETHZürichSwitzerland

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