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arXiv · 2604.27745

Average-Tree Phylogenetic Diversity Parameterized by Scanwidth and Invisibility

Leo van Iersel·Mark Jones·Jannik Schestag·Celine Scornavacca·Mathias Weller
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Abstract

We investigate parameterized algorithms for computing the average-tree phylogenetic diversity (APD) in rooted phylogenetic networks, studying the problem under different structural parameters that capture the deviation of a network from a tree. Our primary parameter is the scanwidth, a measure of the tree-likeness of a given directed acyclic graph. We show that a subset of taxa with maximum APD can be found in polynomial time in phylogenetic networks of scanwidth at most 2, but becomes NP-hard in networks of scanwidth 3. Further, we design an algorithm that computes the APD of a given set of taxa in O(2^sw n) time, where sw denotes the scanwidth and n the number of taxa in the input network. Finally, we give a linear-time algorithm for computing the APD of a given set of taxa if the network induced by these taxa is reticulation-visible. We generalize this algorithm to still run in polynomial time if each biconnected component of the induced network has only constantly many invisible reticulations.

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Leo van Iersel, Mark Jones, Jannik Schestag, Celine Scornavacca, Mathias Weller. 2026-04-30. Average-Tree Phylogenetic Diversity Parameterized by Scanwidth and Invisibility. https://arxiv.org/abs/2604.27745

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