# Maximum-scoring path sets on pangenome graphs of constant treewidth

## TL;DR

This paper introduces a new algorithm for finding maximum-scoring path sets on pangenome graphs with constant treewidth, extending a previous problem from sequences to graphs.

## Contribution

The novel contribution is an algorithm for solving maximum-scoring path sets on graphs with constant treewidth in linear time.

## Key findings

- The algorithm generalizes maximum-scoring segment sets from sequences to graphs.
- It can be applied to pangenome graphs for various biological analyses like CpG islands or ChIP-seq data.
- The approach is efficient for graphs with constant treewidth.

## Abstract

We generalize a problem of finding maximum-scoring segment sets, previously studied by Csűrös (IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2004, 1, 139–150), from sequences to graphs. Namely, given a vertex-weighted graph G and a non-negative startup penalty c, we can find a set of vertex-disjoint paths in G with maximum total score when each path’s score is its vertices’ total weight minus c. We call this new problem maximum-scoring path sets (MSPS). We present an algorithm that has a linear-time complexity for graphs with a constant treewidth. Generalization from sequences to graphs allows the algorithm to be used on pangenome graphs representing several related genomes and can be seen as a common abstraction for several biological problems on pangenomes, including searching for CpG islands, ChIP-seq data analysis, analysis of region enrichment for functional elements, or simple chaining problems.