Hypergraph covering problems motivated by genome assembly questions

TL;DR

This paper explores hypergraph covering problems related to genome assembly, introducing variants of the C1P with multiplicity and providing algorithms to solve them efficiently.

Contribution

It introduces variants of the C1P with multiplicity tailored for genome assembly and offers polynomial-time or fixed-parameter algorithms for these problems.

Findings

Variants of the mC1P are formulated for genome assembly.

Polynomial-time algorithms are developed for certain cases.

Fixed-parameter algorithms are provided for complex variants.

Abstract

The Consecutive-Ones Property (C1P) is a classical concept in discrete mathematics that has been used in several genomics applications, from physical mapping of contemporary genomes to the assembly of ancient genomes. A common issue in genome assembly concerns repeats, genomic sequences that appear in several locations of a genome. Handling repeats leads to a variant of the C1P, the C1P with multiplicity (mC1P), that can also be seen as the problem of covering edges of hypergraphs by linear and circular walks. In the present work, we describe variants of the mC1P that address specific issues of genome assembly, and polynomial time or fixed-parameter algorithms to solve them.