On the consecutive ones property

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

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 Test for the Consecutive Ones Property on Noisy Data

A (0,1)-matrix satisfies the consecutive ones property (COP) for the rows if there exists a column permutation such that the ones in each row of the resulting matrix are consecutive. The consecutive ones test is useful for DNA sequence assembly, for example, in the STS content mapping of YAC library, and in the Bactig assembly based on STS as well as EST

Set covering with almost consecutive ones property

In this paper we consider set covering problems with a coefficient matrix almost having the consecutive ones property, i.e., in many rows of the coefficient matrix, the ones appear consecutively. If this property holds for all rows it is well known that the set covering problem can be solved efficiently. For our case of almost consecutive ones we present a reformulation exploiting the consecuti...