The simultaneous consecutive ones problem

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,...

A Spectral Algorithm for Seriation and the Consecutive Ones Problem

In applications ranging from DNA sequencing through archeological dating to sparse matrix reordering, a recurrent problem is the sequencing of elements in such a way that highly correlated pairs of elements are near each other. That is, given a correlation function f reflecting the desire for each pair of elements to be near each other, find all permutations π with the property that if π(i) < π...

A note on the Consecutive Ones Submatrix problem

A binary matrix has the Consecutive Ones Property (C1P) for columns if there exists a permutation of its rows that leaves the 1’s consecutive in every column. The problem of Consecutive Ones Property for a matrix is a special variant of Consecutive Ones Submatrix problem in which a positive integer K is given and we want to know if there exists a submatrix B of A consisting of K columns of A wi...

Consecutive Ones and a Betweenness Problem in Computational Biology

In this paper we consider a variant of the betweenness problem occurring in computational biology. We present a new polyhedral approach which incorporates the solution of consecutive ones problems and show that it supersedes an earlier one. A particular feature of this new branch-and-cut algorithm is that it is not based on an explicit integer programming formulation of the problem and makes us...

Consecutive Ones Property