Best-first search for treewidth

Finding the exact treewidth of a graph is central to many operations in a variety of areas, including probabilistic reasoning and constraint satisfaction. Treewidth can be found by searching over the space of vertex elimination orders. This search space differs from those where best-first search is typically applied, because a solution path is evaluated by its maximum edge cost instead of the sum of its edge costs. We show how to make best-first search admissible on max-cost problem spaces. We also employ breadth-first heuristic search to reduce the memory requirement while still eliminating all duplicate nodes in the search space. Our empirical results show that our algorithms find the exact treewidth an order of magnitude faster than the previous state-of-the-art algorithm on hard benchmark graphs.