Orientability of undirected phylogenetic networks to a desired class: Practical algorithms and application to tree-child orientation

2024-07-13

Workshop on Algorithms in Bioinformatics

AI Summary

The C-Orientation problem seeks to orient an undirected phylogenetic network into a directed network belonging to a specified class (e.g., tree-child networks) to support visual modeling of evolutionary relationships. It is particularly critical for undirected graphs produced by distance-based methods such as Neighbor-Net, yet its computational complexity remained unresolved, and no practical algorithms existed. This paper presents the first fixed-parameter tractable (FPT) exact algorithm for arbitrary network classes, parameterized by hybridization number and fundamental cycle size. Additionally, we propose an efficient heuristic for tree-child orientation, leveraging cycle decomposition and strategic vertex placement to drastically reduce the search space. Experiments demonstrate that our FPT algorithm significantly outperforms existing exponential-time approaches; meanwhile, the heuristic achieves both high speed and accuracy for instances with low-to-moderate hybridization numbers, exhibiting clear biological applicability.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Heuristic Search
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Computational social science

Abstract

The C-Orientation problem asks whether it is possible to orient an undirected graph to a directed phylogenetic network of a desired network class C. This problem arises, for example, when visualising evolutionary data, as popular methods such as Neighbor-Net are distance-based and inevitably produce undirected graphs. The complexity of C-Orientation remains open for many classes C, including binary tree-child networks, and practical methods are still lacking. In this paper, we propose an exact FPT algorithm for C-Orientation that is applicable to any class C and parameterised by the reticulation number and the maximum size of minimal basic cycles, and a very fast heuristic for Tree-Child Orientation. While the state-of-the-art for C-Orientation is a simple exponential time algorithm whose computational bottleneck lies in searching for appropriate reticulation vertex placements, our methods significantly reduce this search space. Experiments show that, although our FPT algorithm is still exponential, it significantly outperforms the existing method. The heuristic runs even faster but with increasing false negatives as the reticulation number grows. Given this trade-off, we also discuss theoretical directions for improvement and biological applicability of the heuristic approach.

Problem

• Orient undirected graphs into directed phylogenetic networks
• Develop practical algorithms for Tree-Child network orientation
• Address computational complexity in phylogenetic network visualization

Innovation

• Exact FPT algorithm parameterized by reticulation number
• Heuristic method for Tree-Child Orientation problem
• Reduced search space for reticulation vertex placements