rankingtopk_IEEEpreprint.pdf (3.25 MB)

Download file# Ranking top-k trees in tree-based phylogenetic networks

Tree-based phylogenetic networks provide a powerful model for representing complex data or non-tree-like evolution. Such networks consist of an underlying evolutionary tree called a "support tree" (also known as a "subdivision tree") together with extra arcs added between the edges of that tree. However, a tree-based network can have exponentially many support trees, and this leads to a variety of computational problems. Recently, Hayamizu established a theory called the structure theorem for rooted binary phylogenetic networks and provided linear-time and linear-delay algorithms for different problems, such as counting, optimization, and enumeration of support trees. However, in practice, it is often more useful to search for both optimal and near-optimal solutions than to calculate only an optimal solution. In the present paper, we thus consider the following problem: Given a tree-based phylogenetic network

*N*where each arc is weighted by its probability, compute the ranking of top-*k*support trees of*N*according to likelihood values. We provide a linear-delay (and hence optimal) algorithm for this problem.## Funding

### JST PRESTO Grant Numbers JPMJPR16EB and JPMJPR1929

### JSPS KAKENHI 19K22841 and 20H05967

## History

## Email Address of Submitting Author

hayamizu@waseda.jp## ORCID of Submitting Author

0000-0001-8825-6331## Submitting Author's Institution

Department of Applied Mathematics, Waseda University## Submitting Author's Country

- Japan