New Algorithms on Rooted Triplet Consistency

TL;DR

This paper introduces two heuristic algorithms for constructing the maximum consensus rooted phylogenetic tree from triplet data, improving speed and average performance despite the problem's APX-hardness.

Contribution

The paper presents two new heuristic algorithms, FastTree and BPMTR, with improved computational efficiency and average performance for rooted triplet consensus tree construction.

Findings

FastTree runs in O(mn^2) and is faster than previous algorithms.

BPMTR runs in O(mn^3) and outperforms existing approximation algorithms on average.

The problem remains APX-hard, indicating inherent computational difficulty.

Abstract

An evolutionary tree (phylogenetic tree) is a binary, rooted, unordered tree that models the evolutionary history of currently living species in which leaves are labeled by species. In this paper, we investigate the problem of finding the maximum consensus evolutionary tree from a set of given rooted triplets. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corresponding three species. The mentioned problem is known to be APX-hard. We present two new heuristic algorithms. For a given set of m triplets on n species, the FastTree algorithm runs in O(mn^2) which is faster than any other previously known algorithms, although, the outcome is less satisfactory. The BPMTR algorithm runs in O(mn^3) and in average performs better than any other previously known approximation algorithms for this problem.