2009/12/02 by Cédric Chauve, Chauve, Cedric, Ján Maňuch +3
Computer Science · Engineering · #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Metal Forming Simulation Techniques #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0912.0309
openalex publication_date 2009/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by problems of comparative genomics and paleogenomics, in [Chauve et al., 2009], the authors introduced the Gapped Consecutive-Ones Property Problem (k,delta)-C1P: given a binary matrix M and two integers k and delta, 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 delta zeros. The classical C1P problem, which is known to be polynomial is equivalent to the (1,0)-C1P problem. They showed that the (2,delta)-C1P Problem is NP-complete for all delta >= 2 and that the (3,1)-C1P problem is NP-complete. They also conjectured that the (k,delta)-C1P Problem is NP-complete for k >= 2, delta >= 1 and (k,delta) =/= (2,1). Here, we prove that this conjecture is true. The only remaining case is the (2,1)-C1P Problem, which could be polynomial-time solvable.