Two continuous formulations of the maximum independent set problem on a gra
ph G=(V,E) are considered. Both cases involve the maximization of an n-vari
able 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 consider
ed. Given any solution to x(0) in the hypercube, we propose two polynomial-
time algorithms based on these formulations, for finding maximal independen
t sets with cardinality greater than or equal to F(x(0)) and H(x(0)), respe
ctively. A relation between the two approaches is studied and a more genera
l statement for dominating sets is proved. Results of preliminary computati
onal experiments for some of the DIMACS clique benchmark graphs are present
ed.