This note introduces the exact solver Bute for the exact treedepth problem, along with two variants of the solver . Each of these solvers computes an elimination tree  in a bottom-up fashion by finding sets of vertices that induce subgraphs of small treedepth, then combining sets of vertices together with a root vertex to produce larger sets. The algorithms make use of a trie data structure to reduce the effort required to determine acceptable combinations of subtrees. Bute-Plus and Bute-Plus-Plus add a heuristic presolve step , which can quickly find a treedepth decomposition of optimal depth for many instances.
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.
R
the exact solver Bute for the exact treedepth problem, along with two variants
Bute-Plus, an exact solver for the treedepth problem. The core
R
. Each of these solvers computes
is a positive-instance driven dynamic program that constructs
A
of minimum depth
R
by finding sets of vertices that induce subgraphs of small treedepth, then combining sets of vertices together with a root vertex to produce larger sets. The algorithms make use of a
. Three features greatly improve the algorithm's run time. The first of these is a specialised
R
to reduce the effort required to determine acceptable combinations of subtrees. Bute-Plus and Bute-Plus-Plus add a
. The second is a domination rule. The third is a
D
, which