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

DC programming and DCA; Exact penalty; Minimum dominating set; Continuous domain; Continuous optimization; D-C programming; DC algorithm; Exact penalties; Finite number; Integer solutions; Linear programs; Optimization approach; Set problems; Standard method; Computer Science Applications; Discrete Mathematics and Combinatorics; Control and Optimization; Computational Theory and Mathematics; Applied Mathematics

Abstract :

[en] 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. © Springer Science+Business Media, LLC 2011.

Disciplines :

Computer science

Author, co-author :

SCHLEICH, Julien ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)

An Le Thi, Hoai; LITA, University Paul Verlaine-Metz, 57045 Metz, France

BOUVRY, Pascal ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)

External co-authors :

yes

Language :

English

Title :

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

Publication date :

November 2012

Journal title :

Journal of Combinatorial Optimization

ISSN :

1382-6905

eISSN :

1573-2886

Publisher :

Springer Science and Business Media LLC

Volume :

Issue :

Pages :

397 - 412

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://link.springer.com/content/pdf/10.1007/s10878-011-9396-0.pdf

Available on ORBilu :

since 21 November 2023

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