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

Authors:
Julien Schleich;Hoai An Le Thi;Pascal Bouvry
Affiliations:
SnT Interdisciplinary Center, University of Luxembourg, Kirchberg Campus, Luxembourg;LITA, University Paul Verlaine--Metz, Metz, France 57045;FSTC---CSC, University of Luxembourg, Kirchberg Campus, Luxembourg
Venue:
Journal of Combinatorial Optimization
Year:
2012

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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.