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- Ján Maňuch, Murray Patterson, Roland Wittler, Cedric Chauve, Eric Tannier
- BMC Bioinformatics
- 2012

Recovering the structure of ancestral genomes can be formalized in terms of properties of binary matrices such as the Consecutive-Ones Property (C1P). The Linearization Problem asks to extract, from a given binary matrix, a maximum weight subset of rows that satisfies such a property. This problem is in general intractable, and in particular if the… (More)

Mitchell and Ternovska [49, 50] propose a constraint programming framework for search problems that is based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX). In this framework, the problem is encoded in a logic, an instance of the problem is represented by a finite structure, and… (More)

In comparative genomics, differences or similarities of gene orders are determined to predict functional relations of genes or phylogenetic relations of genomes. For this purpose, various combinatorial models can be used to specify gene clusters--groups of genes that are co-located in a set of genomes. Several approaches have been proposed to reconstruct… (More)

Motivated by problems of comparative genomics and paleogenomics, we introduce the Gapped Consecutive-Ones Property Problem (k,δ)-C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k sequences of 1's and no two consecutive sequences of 1's are separated by a gap of more than δ 0's. The… (More)

- Murray Patterson, Tobias Marschall, Nadia Pisanti, Leo van Iersel, Leen Stougie, Gunnar W. Klau +1 other
- RECOMB
- 2014

A binary matrix has the Consecutive-Ones Property (C1P) if its columns can be ordered in such a way that all 1's in each row are consecutive. We consider here a variant of the C1P where columns can appear multiple times in the ordering. Although the general problem of deciding the C1P with multiplicity is NP-complete, we present here a case of interest in… (More)

- Murray Patterson, Gergely Szöllősi, Vincent Daubin, Eric Tannier
- BMC Bioinformatics
- 2013

Models of ancestral gene order reconstruction have progressively integrated different evolutionary patterns and processes such as unequal gene content, gene duplications, and implicitly sequence evolution via reconciled gene trees. These models have so far ignored lateral gene transfer, even though in unicellular organisms it can have an important… (More)

Motivated by problems of comparative genomics and pale-ogenomics, in [6] the authors introduced the Gapped Consecutive-Ones Property Problem (k, δ)-C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k blocks of ones and no two consecutive blocks of ones are separated by a gap of more… (More)

The Gapped Consecutive-Ones Property (C1P) Problem, or the (k, δ)-C1P Problem is: given a binary matrix M and integers k and δ, decide if the columns of M can be ordered such that each row contains at most k blocks of 1's, and no two neighboring blocks of 1's are separated by a gap of more than δ 0's. This problem was introduced by Chauve et al. ( 2009b ).… (More)