An Algorithm for the Exact Treedepth Problem

Abstract

We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree, along with symmetry-breaking and domination rules. We present an empirical study showing that the algorithm outperforms the current state-of-the-art solver (which is based on a SAT encoding) by orders of magnitude on a range of graph classes.

14 pages, 6 figures, 2 tables. This is an extended version of a paper to appear in the proceedings of SEA 2020. The arXiv version is the conference version plus Appendix A (a correctness proof)