PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth

TL;DR

Bute-Plus is an exact bottom-up solver for treedepth that uses advanced data structures, domination rules, and heuristics to efficiently find optimal solutions for various instances.

Contribution

It introduces Bute-Plus, a novel solver employing a positive-instance driven dynamic programming approach with specialized data structures and heuristics for treedepth.

Findings

Significantly improves run time for treedepth problems

Effective heuristic presolve for many instances

Utilizes specialized trie data structure and domination rules

Abstract

This note introduces Bute-Plus, an exact solver for the treedepth problem. The core of the solver is a positive-instance driven dynamic program that constructs an elimination tree of minimum depth in a bottom-up fashion. Three features greatly improve the algorithm's run time. The first of these is a specialised trie data structure. The second is a domination rule. The third is a heuristic presolve step can quickly find a treedepth decomposition of optimal depth for many instances.