Unique perfect phylogeny is NP-hard

TL;DR

This paper proves that determining whether a given ternary phylogenetic tree is uniquely defined by a set of quartet subtrees is an NP-hard problem, confirming its computational complexity.

Contribution

It establishes the NP-hardness of the problem of verifying the uniqueness of a phylogenetic tree based on quartet data, answering a longstanding open question.

Findings

Proves the NP-hardness of the unique perfect phylogeny problem

Confirms computational difficulty in phylogenetic tree reconstruction

Addresses a question posed by Mike Steel in phylogenetics

Abstract

We answer, in the affirmative, the following question proposed by Mike Steel as a $100 challenge: "Is the following problem NP-hard? Given a ternary phylogenetic X-tree T and a collection Q of quartet subtrees on X, is T the only tree that displays Q ?"