MaxSAT-Based Postprocessing for Treedepth

Abstract

Treedepth is an increasingly popular graph invariant. Many NP-hard combinatorial problems can be solved efficiently on graphs of bounded treedepth. Since the exact computation of treedepth is itself NP-hard, recent research has focused on the development of heuristics that compute good upper bounds on the treedepth. In this paper, we introduce a novel MaxSAT-based approach for improving a heuristically obtained treedepth decomposition. At the core of our approach is an efficient MaxSAT encoding of a weighted generalization of treedepth arising naturally due to subtree contractions. The encoding is applied locally to the given treedepth decomposition to reduce its depth, in conjunction with the collapsing of subtrees. We show the local improvement method’s correctness and provide an extensive experimental evaluation with some encouraging results.