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

Julien Schleich (), Hoai An Le Thi () and Pascal Bouvry ()
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Julien Schleich: University of Luxembourg
Hoai An Le Thi: University Paul Verlaine—Metz
Pascal Bouvry: University of Luxembourg

Journal of Combinatorial Optimization, 2012, vol. 24, issue 4, No 1, 397-412

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9396-0

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