Efficient Reconstruction of Arboreal Networks

2026-05-01

AI Summary

This study addresses the problem of efficiently reconstructing multi-rooted phylogenetic networks with an underlying tree-like structure, known as arboreal networks. For stack-free arboreal networks, the work proposes a combinatorial encoding scheme based on rooted triples augmented with a novel structural unit termed a “duet,” and establishes a complete triple–duet system. Building upon this framework, a polynomial-time reconstruction algorithm is developed to exactly and efficiently recover arboreal networks. Theoretical analysis and classification results confirm the correctness and effectiveness of the approach. Notably, the introduction of the “duet” concept provides a natural metric framework for multi-rooted networks, constituting the primary innovation of this work.

Abstract

Arboreal networks are multi-rooted phylogenetic networks whose underlying graph is a tree. We give an encoding of stack-free arboreal networks in terms of triplets and the novel concept of a duet. This yields a polynomial time algorithm to construct these networks from complete triplet and duet systems. The classification results show correctness and lead to a natural metric on these multi-rooted networks.

Problem

• arboreal networks
• phylogenetic networks
• triplets
• duets
• network reconstruction

Innovation

• arboreal networks
• triplets
• duets
• polynomial time algorithm
• phylogenetic reconstruction