Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

TL;DR

This paper introduces cyclic generators and an enhanced linear kernel for the rooted subtree prune and regraft (rSPR) distance, significantly reducing the kernel size from exponential to linear in the parameter k, improving computational efficiency.

Contribution

The paper presents a novel linear kernel for rSPR distance using cyclic generators and an augmented reduction rule, achieving a tight bound of 9k-3 leaves, improving over previous methods.

Findings

Linear kernel size improved to 9k-3 leaves

Introduction of cyclic generators for phylogenetic trees

Enhanced kernel for the hybridization problem

Abstract

The rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a well-studied measure of topological dissimilarity that is NP-hard to compute. Here we describe an improved linear kernel for the problem. In particular, we show that if the classical subtree and chain reduction rules are augmented with a modified type of chain reduction rule, the resulting trees have at most 9k-3 leaves, where k is the rSPR distance; and that this bound is tight. The previous best-known linear kernel had size O(28k). To achieve this improvement we introduce cyclic generators, which can be viewed as cyclic analogues of the generators used in the phylogenetic networks literature. As a corollary to our main result we also give an improved weighted linear kernel for the minimum hybridization problem on two rooted binary phylogenetic trees.