FPT algorithms solve two budgeted PD variants on networks in O*(2^nsw B^2) time and compute PD scores for the third in O*(3^nsw) time, plus exact nsw computation via DP and ILP.
arXiv , jorunal =:2602.06903 , TODOdoi =
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An O(4^{k + k log k} n + n m^2)-time algorithm for TREE CONTAINMENT parameterized by scanwidth k of a given tree-extension, with a matching ETH lower bound of no 2^{o(c log c)} n^{O(1)} algorithm for directed cutwidth c even on binary inputs.
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Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth
FPT algorithms solve two budgeted PD variants on networks in O*(2^nsw B^2) time and compute PD scores for the third in O*(3^nsw) time, plus exact nsw computation via DP and ILP.
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Tree Containment Parameterized by Scanwidth
An O(4^{k + k log k} n + n m^2)-time algorithm for TREE CONTAINMENT parameterized by scanwidth k of a given tree-extension, with a matching ETH lower bound of no 2^{o(c log c)} n^{O(1)} algorithm for directed cutwidth c even on binary inputs.