Minimal Conflicting Sets for the Consecutive Ones Property in ancestral genome reconstruction

TL;DR

This paper introduces algorithms for identifying minimal conflicting sets in binary matrices with the Consecutive Ones Property, aiding ancestral genome reconstruction by distinguishing true positives from false positives.

Contribution

It presents a polynomial-time algorithm for detecting rows in minimal conflicting sets and reduces the problem to boolean clause generation, advancing combinatorial analysis in genomics.

Findings

Algorithms effectively identify minimal conflicting sets in simulated genomic data.

Method distinguishes true positive from false positive ancestral syntenies.

Application to yeast genomes assesses reliability of ancestral genome proposals.

Abstract

A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1's on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in comparative genomics applications, but very little is known about their combinatorial structure and efficient algorithms to compute them. We first describe an algorithm that detects rows that belong to Minimal Conflicting Sets. This algorithm has a polynomial time complexity when the number of 1's in each row of the considered matrix is bounded by a constant. Next, we show that the problem of computing all Minimal Conflicting Sets can be reduced to the joint generation of all minimal true clauses and maximal false clauses for some monotone boolean function. We use these methods on simulated data related to ancestral genome reconstruction to show that computing Minimal Conflicting Set is useful in discriminating between true positive and false positive ancestral syntenies. We also study a dataset of yeast genomes and address the reliability of an ancestral genome proposal of the Saccahromycetaceae yeasts.