Abstract
A binary matrix has the Consecutive Ones Property (C1P) if there exists a permutation of its columns (i.e. a sequence of column swappings) such that in the resulting matrix the 1s are consecutive in every row. A Minimal Conflicting Set (MCS) of rows is a set of rows \(\mathcal{R}\) that does not have the C1P, but such that any proper subset of \(\mathcal{R}\) has the C1P. In [5], Chauve et al. gave a O(Δ2 m max (4,Δ + 1) (n + m + e)) time algorithm to decide if a row of a m ×n binary matrix with at most Δ 1s per row belongs to at least one MCS of rows. Answering a question raised in [2], [5] and [25], we present the first polynomial-time algorithm to decide if a row of a m ×n binary matrix belongs to at least one MCS of rows.
Partially founded by ANR Project 2010 JCJC SIMI 2 BIRDS.
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Blin, G., Rizzi, R., Vialette, S. (2011). A Polynomial-Time Algorithm for Finding a Minimal Conflicting Set Containing a Given Row. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_29
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DOI: https://doi.org/10.1007/978-3-642-20712-9_29
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