Faster and Simpler Minimal Conflicting Set Identification

Let C be a finite set of n elements and R = {r1, r2, . . . , rm} a family of m subsets of C. A subset X of R verifies the Consecutive Ones Property (C1P) if there exists a permutation P of C such that each ri in X is an interval of P . A Minimal Conflicting Set (MCS) S ⊆ R is a subset of R that does not verify the C1P, but such that any of its proper subsets does. In this paper, we present a new simpler and faster algorithm to decide if a given element r ∈ R belongs to at least one MCS. Our algorithm runs in O(nm+nm), largely improving the current O(mn(m+n) log(m+n)) fastest algorithm of [Blin et al, CSR 2011]. The new algorithm is based on an alternative approach considering minimal forbidden induced subgraphs of interval graphs instead of Tucker matrices.