A Polynomial-Time Algorithm for Finding a Minimal Conflicting Set Containing a Given Row

Guillaume Blin (1) , Romeo Rizzi (2) , Stéphane Vialette (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 DIMI - Dipartimento di Matematica e Informatica - Universita Udine

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 R that does not have the C1P, but such that any proper subset of R has the C1P. In [5], Chauve et al. gave a O(∆2 mmax(4,∆+1) (n + m + e)) time algorithm to decide if a row of a m × n binary matrix with at most ∆ 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.

Domaines: Algorithme et structure de données [cs.DS]; Bio-informatique [q-bio.QM]

Guillaume Blin, Romeo Rizzi, Stéphane Vialette. A Polynomial-Time Algorithm for Finding a Minimal Conflicting Set Containing a Given Row. 6th International Computer Science Symposium in Russia (CSR'11), 2011, St Petersbourg, Russia. pp.373-384, ⟨10.1007/978-3-642-20712-9_29⟩. ⟨hal-00620378⟩