Finding independent sets in a graph using continuous multivariable polynomial formulations

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(x(0)) and H(x(0)), 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.