On the treewidth of NK landscapes

Authors:
Yong Gao;Joseph Culberson
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada
Venue:
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Year:
2003

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Abstract

The concepts of treewidth and tree-decomposition on graphs generalize those of the trees. It is well established that when restricted to instances with a bounded treewidth, many NP hard problems can be solved polynomially. In this paper, we study the treewidth of the NK landscape models. We show that the NK landscape model with adjacent neighborhoods has a constant treewidth, and prove that for k ≥ 2, the treewidth of the NK landscape model with random neighborhoods asymptotically grows with the problem size n.