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 to be polynomial, is equivalent to the (1,0)-C1P Problem. We show that the (2, δ)-C1P Problem is NP-complete for δ ≥ 2. We conjecture that the (k, δ)-C1P Problem is NP-complete for k ≥ 2, δ ≥ 1, (k, δ) ≠ (2, 1). We also show that the (k, δ)-C1P Problem can be reduced to a graph bandwidth problem parameterized by a function of k, δ and of the maximum number s of 1's in a row of M, and hence is polytime solvable if all three parameters are constant. © 2009 Elsevier B.V. All rights reserved

Chauve, C., Maňuch, J., Patterson, M. (2009). On the Gapped Consecutive-Ones Property. In European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009) (pp.121-125) [10.1016/j.endm.2009.07.020].

On the Gapped Consecutive-Ones Property

Patterson, M
2009

Abstract

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 to be polynomial, is equivalent to the (1,0)-C1P Problem. We show that the (2, δ)-C1P Problem is NP-complete for δ ≥ 2. We conjecture that the (k, δ)-C1P Problem is NP-complete for k ≥ 2, δ ≥ 1, (k, δ) ≠ (2, 1). We also show that the (k, δ)-C1P Problem can be reduced to a graph bandwidth problem parameterized by a function of k, δ and of the maximum number s of 1's in a row of M, and hence is polytime solvable if all three parameters are constant. © 2009 Elsevier B.V. All rights reserved
paper
algorithm; computational complexity; consecutive-ones property; Discrete Mathematics and Combinatorics; Applied Mathematics
English
European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009) 7-11 September
2009
European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009)
2009
34
121
125
reserved
Chauve, C., Maňuch, J., Patterson, M. (2009). On the Gapped Consecutive-Ones Property. In European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009) (pp.121-125) [10.1016/j.endm.2009.07.020].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/217383
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