SAT-Based Approaches to Treewidth Computation: An Evaluation

Tree width is an important structural property of graphs, tightly connected to computational tractability in eg various constraint satisfaction formalisms such as constraint programming, Boolean satisfiability, and answer set programming, as well as probabilistic inference, for instance. An obstacle to harnessing tree width as a way to efficiently solving bounded tree width instances of NP-hard problems is that deciding tree width, and hence computing an optimal tree-decomposition, is in itself an NP-complete problem. In this paper, we study the applicability of Boolean satisfiability (SAT) based approaches to determining the tree widths of graphs, and at the same time obtaining an associated optimal tree-decomposition. Extending earlier studies, we evaluate various SAT and Max SAT based strategies for tree width computation, and compare these approaches to practical dedicated exact algorithms for the problem.