Computing Rooted and Unrooted Maximum Consistent Supertrees

TL;DR

This paper introduces exact algorithms for constructing maximum consistent supertrees from triplets and quartets, applicable to rooted and unrooted trees, with improvements in efficiency and polynomial space implementation.

Contribution

It presents novel exact algorithms for maximum consistent supertrees from triplets and quartets, extending to weighted cases and optimizing space complexity.

Findings

Algorithms run in exponential time with respect to input size

Polynomial space algorithms are developed for practical use

Maximum consistent trees can be computed efficiently for large sets

Abstract

A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary trees on four leaves. We give exact algorithms constructing rooted and unrooted maximum consistent supertrees in time O(2^n n^5 m^2 log(m)) for a set of m triplets (quartets), each one distinctly leaf-labeled by some subset of n labels. The algorithms extend to weighted triplets (quartets). We further present fast exact algorithms for constructing rooted and unrooted maximum consistent trees in polynomial space. Finally, for a set T of m rooted or unrooted trees with maximum degree D and distinctly leaf-labeled by some subset of a set L of n labels, we compute, in O(2^{mD} n^m m^5 n^6 log(m)) time, a tree distinctly leaf-labeled by a maximum-size subset X of L that all trees in T, when restricted to X, are consistent with.