Domination analysis of combinatorial optimization problems

@article{Gutin2003DominationAO,
  title={Domination analysis of combinatorial optimization problems},
  author={Gregory Gutin and Alek Vainshtein and Anders Yeo},
  journal={Discrete Applied Mathematics},
  year={2003},
  volume={129},
  pages={513-520}
}
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 proved already in the 1970’s 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.