On Robinsonian dissimilarities, the consecutive ones property and latent variable models

On Robinsonian dissimilarities, the consecutive ones property and latent variable models

A dissimilarity measure on a set of objects is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. The Robinson property of a dissimilarity reflects an order of the objects. If a dissimilarity is not observed directly, it must be obtained from the data. Given that an ordinal structure is as...

On the Gapped Consecutive-Ones Property

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 classical C1P problem, which is known ...

Consecutive Ones Property

Consecutive Ones Property and Spectral Ordering

A 0-1 matrix where in each column the 1s occur consecutively is said to have the consecutive ones property. This property and its approximations are important in a variety of applications, e.g., in DNA analysis and paleontology. Checking whether the matrix rows can be permuted so that this property holds can be done in polynomial time. However, an exact solution rarely exists in applications. T...

Hardness results on the gapped consecutive-ones property problem

Motivated by problems of comparative genomics and paleogenomics, 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 than δ zeros. The classical C1P problem,...