Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA
- 221 Downloads
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.
KeywordsDC programming and DCA Exact penalty Minimum dominating set
Unable to display preview. Download preview PDF.
- Dutot A, Guinand F, Olivier D, Pigné Y (2007) Graphstream: A tool for bridging the gap between complex systems and dynamic graphs. In: EPNACS: Emergent properties in natural and artificial complex systems Google Scholar
- Erdős P, Rényi A (1959) On random graphs. Publ Math 6:290–297 Google Scholar
- Garey M, Johnson DS (1990) Computers and intractability; A guide to the theory of NP-completeness. Freeman, San Francisco Google Scholar
- Gaspers S, Kratsch D, Liedloff M (2006) Exponential time algorithms for the minimum dominating set problem. In: Proceedings of SWAT, vol 4059, pp 148–159 Google Scholar
- van Rooij JMM, Bodlaender HL (2008) Design by measure and conquer: A faster exact algorithm for dominating set. In: Proceedings of STACS, pp 657–668 Google Scholar
- Wu J, Cardei M, Dai F, Yang S (2005) Extended dominating set in ah hoc networks using cooperative communication. In: Networking. LNCS, vol 3462, pp 1393–1396 Google Scholar