Abstract
Two continuous formulations of the maximum independent set problem on a graph G=(V,E) are considered. Both cases involve the maximization of an n-variable polynomial over the n-dimensional hypercube, where n is the number of nodes in G. Two (polynomial) objective functions F(x) and H(x) are considered. Given any solution to x 0 in the hypercube, we propose two polynomial-time algorithms based on these formulations, for finding maximal independent sets with cardinality greater than or equal to F(x0) and H(x0), respectively. A relation between the two approaches is studied and a more general statement for dominating sets is proved. Results of preliminary computational experiments for some of the DIMACS clique benchmark graphs are presented.
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Abello, J., Butenko, S., Pardalos, P.M. et al. Finding independent sets in a graph using continuous multivariable polynomial formulations. Journal of Global Optimization 21, 111–137 (2001). https://doi.org/10.1023/A:1011968411281
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DOI: https://doi.org/10.1023/A:1011968411281