A heuristic use of dynamic programming to upperbound treewidth [article]

Hisao Tamaki
2019 arXiv   pre-print
For a graph G, let Π(G) denote the set of all potential maximal cliques of G. For each subset Π of Π(G), let (G, Π) denote the smallest k such that there is a tree-decomposition of G of width k whose bags all belong to Π. Bouchitté and Todinca observed in 2001 that (G, Π(G)) is exactly the treewidth of G and developed a dynamic programming algorithm to compute it. Indeed, their algorithm can readily be applied to an arbitrary non-empty subset Π of Π(G) and computes (G, Π), or reports that it is
more » ... undefined, in time |Π||V(G)|^O(1). This efficient tool for computing (G, Π) allows us to conceive of an iterative improvement procedure for treewidth upper bounds which maintains, as the current solution, a set of potential maximal cliques rather than a tree-decomposition. We design and implement an algorithm along this approach. Experiments show that our algorithm vastly outperforms previously implemented heuristic algorithms for treewidth.
arXiv:1909.07647v2 fatcat:r7nj7vtzljemfnecsehvw6q3ya