An Iterative Heuristic Algorithm for Tree Decomposition

Many instances of NP-hard problems can be solved efficiently if the treewidth of their corresponding graph is small. Finding the optimal tree decompositions is an NP-hard problem and different algorithms have been proposed in the literature for generation of tree decompositions of small width. In this paper is presented new iterated local search algorithm to find good upper bounds for treewidth of an undirected graph. The iterated local search algorithm consist from construction phase, and includes the mechanism for perturbation of solution, and the mechanism for accepting of solution for the next iteration. In the construction phase the solutions are generated by the heuristics which searches for good elimination ordering of nodes of graph, based on moving of only vertices that produce the largest clique in the elimination process. We proposed and evaluated different perturbation mechanisms and acceptance criteria. The proposed algorithms are tested on DIMACS instances for vertex coloring, and they are compared with the existing approaches in literature. The described algorithms have a good time performance and for several instances improve the best existing upper bounds for the treewidth. 1Technische Universität Wien mailto: [email protected] Copyright c © 2007 by the authors TECHNICAL REPORT DBAI-TR-2007-56 2