Complementary approaches for the computation of the independent number of a graph

Authors:
Carmo P. Brás;Joaquim J. Júdice
Affiliations:
CMA, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Departamento de Matemática, Caparica, Portugal;Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Departamento de Matemática and Instituto de Telecomunicações, Coimbra, Portugal
Venue:
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Year:
2009

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Abstract

The problem of finding the independent number of an undirected graph is formulated as two equivalent Mathematical Programs with Linear Complementarity Constraints (MPLCC). A multistarting Lemke's method is introduced for dealing with the first formulation and is able to find a good approximate of the independent number in a finite number of iterations. A sequential complementary algorithm is also discussed for the second formulation and can find the independent number at least in theory. Some computational experience is included to highlight the efficacy of the complementary approaches for computing the independent number of graphs from the Dimacs collection.