Faster and simpler minimal conflicting set identification

Abstract

Let be a finite set of n elements and a family of m subsets of . A subset of satisfies the Consecutive Ones Property (C1P) if there exists a permutation P of such that each r i in is an interval of P. A Minimal Conflicting Set (MCS) is a subset of that does not satisfy 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 belongs to at least one MCS. Our algorithm runs in O(n 2 m 2 + nm 7), largely improving the current O(m 6 n 5 (m + n) 2 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. © 2012 Springer-Verlag.