Exact and Heuristic Computation of the Scanwidth of Directed Acyclic Graphs
arxiv(2024)
摘要
To measure the tree-likeness of a directed acyclic graph (DAG), a new width
parameter that considers the directions of the arcs was recently introduced:
scanwidth. We present the first algorithm that efficiently computes the exact
scanwidth of general DAGs. For DAGs with one root and scanwidth k it runs in
O(k · n^k · m) time. The algorithm also functions as an FPT algorithm
with complexity O(2^4 ℓ - 1·ℓ· n + n^2) for phylogenetic
networks of level-ℓ, a type of DAG used to depict evolutionary
relationships among species. Our algorithm performs well in practice, being
able to compute the scanwidth of synthetic networks up to 30 reticulations and
100 leaves within 500 seconds. Furthermore, we propose a heuristic that obtains
an average practical approximation ratio of 1.5 on these networks. While we
prove that the scanwidth is bounded from below by the treewidth of the
underlying undirected graph, experiments suggest that for networks the
parameters are close in practice.
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