Efficiently Inferring Pairwise Subtree Prune-and-Regraft Adjacencies between Phylogenetic Trees

TL;DR

This paper presents a time-optimal algorithm for constructing SPR graphs among phylogenetic trees, significantly improving efficiency and enabling large-scale analysis of tree relationships.

Contribution

It introduces the first time-optimal $O(mn^2)$ algorithm for SPR graph construction and efficient algorithms for NNI and TBR graphs, advancing phylogenetic analysis tools.

Findings

Achieved $O(mn^2)$ time complexity for SPR graph construction

Enabled analysis of larger phylogenetic tree collections

Provided efficient algorithms for NNI and TBR graphs

Abstract

We develop a time-optimal $O(mn^2)$-time algorithm to construct the subtree prune-regraft (SPR) graph on a collection of m phylogenetic trees with n leaves. This improves on the previous bound of $O(mn^3)$. Such graphs are used to better understand the behaviour of phylogenetic methods and recommend parameter choices and diagnostic criteria. The limiting factor in these analyses has been the difficulty in constructing such graphs for large numbers of trees. We also develop the first efficient algorithms for constructing the nearest-neighbor interchange (NNI) and tree bisection-and-reconnection (TBR) graphs