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On locally optimal independent sets and vertex covers

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  • Gang Yu
  • Olivier Goldschmidt

Abstract

In this paper, we introduce a new notion of local optimality and demonstrate its application to the problem of finding optimal independent sets and vertex covers in k‐claw free graphs. The maximum independent set problem in k‐claw free graphs has interesting applications in the design of electronic testing fixtures for printed circuit boards [13]. For this problem, our concept of local optimality enabled us to devise an efficient heuristic algorithm which outperforms the currently best approximation algorithm by nearly a factor of two in terms of worst case bound. We believe that the idea of local optimality suggested in this paper can also be applied to other combinatorial problems such as the clique problem, the dominating set problem and the graph coloring problem. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • Gang Yu & Olivier Goldschmidt, 1996. "On locally optimal independent sets and vertex covers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 737-748, August.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:5:p:737-748
    DOI: 10.1002/(SICI)1520-6750(199608)43:53.0.CO;2-6
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    References listed on IDEAS

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    1. Egon Balas & Vašek Chvátal & Jaroslav Nešetřil, 1987. "On the Maximum Weight Clique Problem," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 522-535, August.
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    Cited by:

    1. Gang Yu & Olivier Goldschmidt, 1997. "Local Optimality and Its Application on Independent Sets for k-claw Free Graphs," Journal of Combinatorial Optimization, Springer, vol. 1(2), pages 151-164, June.

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