Domination analysis of combinatorial optimization problems

Abstract

We use the notion of domination ratio introduced by Glover and Punnen in 1997 to present a new classification of combinatorial optimization (CO) problems: DOM -easy and DOM -hard problems. It follows from results already proved in the 1970s that min TSP (both symmetric and asymmetric versions) is DOM -easy. We prove that several CO problems are DOM -easy including weighted max k- SAT and max cut. We show that some other problems, such as max clique and min vertex cover, are DOM -hard unless P=NP.