Finding independent sets in a graph using continuous multivariable polynomial formulations Academic Article uri icon

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 x0 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.

author list (cited authors)

  • Abello, J., Butenko, S., Pardalos, P. M., & Resende, M.

citation count

  • 34

publication date

  • October 2001