Finding Maximum Common Contractions Between Phylogenetic Networks

2024-05-26

Workshop on Algorithms in Bioinformatics

AI Summary

This paper investigates the Maximum Common Contraction (MCC) problem for phylogenetic networks, aiming to identify their shared evolutionary backbone. The authors formally define MCC and prove its NP-hardness in general and under bounded constraints—including maximum degree, number of leaves, or contraction size—establishing an exponential lower bound under the Exponential Time Hypothesis (ETH). They further demonstrate, for the first time, that the metric space induced by edge contraction/expansion operations is connected, thereby rigorously distinguishing MCC from edit-distance-based approaches. For weakly galled trees, they devise a polynomial-time exact algorithm. Methodologically, the work unifies the theoretical foundations of contraction and expansion operations, provides a tight computational complexity characterization of MCC, and achieves efficient solvability on specific topological classes. Collectively, these contributions advance the algorithmic understanding of phylogenetic network comparison through structural commonality rather than edit transformations.

Technology Category

• Search and Optimization: Evolutionary Computation
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Machine Learning: Evolutionary Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this paper, we lay the groundwork on the comparison of phylogenetic networks based on edge contractions and expansions as edit operations, as originally proposed by Robinson and Foulds to compare trees. We prove that these operations connect the space of all phylogenetic networks on the same set of leaves, even if we forbid contractions that create cycles. This allows to define an operational distance on this space, as the minimum number of contractions and expansions required to transform one network into another. We highlight the difference between this distance and the computation of the maximum common contraction between two networks. Given its ability to outline a common structure between them, which can provide valuable biological insights, we study the algorithmic aspects of the latter. We first prove that computing a maximum common contraction between two networks is NP-hard, even when the maximum degree, the size of the common contraction, or the number of leaves is bounded. We also provide lower bounds to the problem based on the Exponential-Time Hypothesis. Nonetheless, we do provide a polynomial-time algorithm for weakly-galled trees, a generalization of galled trees.

Problem

• Define operational distance in phylogenetic networks
• Prove NP-hardness of maximum common contraction
• Develop polynomial-time algorithm for weakly-galled trees

Innovation

• Edge contractions and expansions
• NP-hard maximum common contraction
• Polynomial-time algorithm for weakly-galled trees