Efficient Enumeration of the Directed Binary Perfect Phylogenies from Incomplete Data

TL;DR

This paper presents an efficient algorithm using zero-suppressed binary decision diagrams for enumerating all possible perfect phylogenies from incomplete binary character data, outperforming traditional branch-and-bound methods.

Contribution

It introduces a novel ZDD-based approach for enumerating perfect phylogenies with incomplete data, improving efficiency over existing methods.

Findings

ZDD approach outperforms branch-and-bound in experiments

Counting consistent phylogenies is #P-complete

Efficient enumeration of all compatible phylogenies is feasible with ZDD

Abstract

We study a character-based phylogeny reconstruction problem when an incomplete set of data is given. More specifically, we consider the situation under the directed perfect phylogeny assumption with binary characters in which for some species the states of some characters are missing. Our main object is to give an efficient algorithm to enumerate (or list) all perfect phylogenies that can be obtained when the missing entries are completed. While a simple branch-and-bound algorithm (B&B) shows a theoretically good performance, we propose another approach based on a zero-suppressed binary decision diagram (ZDD). Experimental results on randomly generated data exhibit that the ZDD approach outperforms B&B. We also prove that counting the number of phylogenetic trees consistent with a given data is #P-complete, thus providing an evidence that an efficient random sampling seems hard.