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Journal of Combinatorial Optimization

, Volume 24, Issue 4, pp 397–412 | Cite as

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

  • Julien Schleich
  • Hoai An Le ThiEmail author
  • Pascal Bouvry
Article

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.

Keywords

DC programming and DCA Exact penalty Minimum dominating set 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Julien Schleich
    • 1
  • Hoai An Le Thi
    • 2
    Email author
  • Pascal Bouvry
    • 3
  1. 1.SnT Interdisciplinary CenterUniversity of LuxembourgKirchberg CampusLuxembourg
  2. 2.LITAUniversity Paul Verlaine—MetzMetzFrance
  3. 3.FSTC–CSCUniversity of LuxembourgKirchberg CampusLuxembourg

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