  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.
