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Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA

Author

Listed:
  • Julien Schleich

    (University of Luxembourg)

  • Hoai An Le Thi

    (University Paul Verlaine—Metz)

  • Pascal Bouvry

    (University of Luxembourg)

Abstract

We propose a new optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) to the so-called Minimum M-Dominating Set problem in graphs. This problem is beforehand re-casted as a polyhedral DC program with the help of exact penalty in DC programming. The related DCA is original and computer efficient because it consists of solving a few linear programs and converges after a finite number of iterations to an integer solution while working in a continuous domain. Numerical simulations show the efficiency and robustness of DCA and its superiority with respect to standard methods.

Suggested Citation

  • Julien Schleich & Hoai An Le Thi & Pascal Bouvry, 2012. "Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 397-412, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9396-0
    DOI: 10.1007/s10878-011-9396-0
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    References listed on IDEAS

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    1. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
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