Minimal Conflicting Sets for the Consecutive Ones Property in Ancestral Genome Reconstruction

Authors:
Cedric Chauve;Utz-Uwe Haus;Tamon Stephen;Vivija P. You
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, Canada;Institute for Mathematical Optimization, University of Magdeburg, Germany;Department of Mathematics, Simon Fraser University, Burnaby, Canada;Department of Mathematics, Simon Fraser University, Burnaby, Canada
Venue:
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
Year:
2009

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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 1s 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 clause and maximal false clauses for some monotone boolean function. We use these methods in preliminary experiments on simulated data related to ancestral genome reconstruction.