Year: 2026
Type: preprint
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 with scanwidth at most 2, but becomes NP-hard in networks with scanwidth at most 3. Further, we design an algorithm that computes the APD of a given set of taxa in $\mathcal{O}(2^{s} \cdot n)$ time, given a width-$s$ tree-extension, with $n$ vertices of 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 an FPT algorithm with respect to the maximum number of invisible reticulations of any biconnected component of the induced network, assuming the indegrees are bounded by a constant.
Source: arXiv (Cornell University)
Institutions: Delft University of Technology, Université Gustave Eiffel
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7159678876
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