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.

中文翻译：

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Bute：树深度的自下而上精确求解器（以用户名 peaty 提交给 PACE 2020）

本笔记介绍了用于精确树深度问题的精确求解器 Bute，以及求解器的两个变体。这些求解器中的每一个都以自底向上的方式计算消除树，方法是找到诱导小树深度子图的顶点集，然后将顶点集与根顶点组合在一起以产生更大的集。该算法使用特里数据结构来减少确定可接受的子树组合所需的工作量。Bute-Plus 和 Bute-Plus-Plus 增加了启发式预求解步骤，可以快速找到多个实例的最优深度的树深度分解。