A new characterization of matrices with the consecutive ones property

Authors:
N. S. Narayanaswamy;R. Subashini
Affiliations:
Indian Institute of Technology Madras, Chennai, India;National Institute of Technology, Calicut, India
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 6
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Abstract

We consider the following constraint satisfaction problem: Given a set F of subsets of a finite set S of cardinality n, and an assignment of intervals of the discrete set {1,...,n} to each of the subsets, does there exist a bijection f:S-{1,...,n} such that for each element of F, its image under f is same as the interval assigned to it. An interval assignment to a given set of subsets is called feasible if there exists such a bijection. In this paper, we characterize feasible interval assignments to a given set of subsets. We then use this result to characterize matrices with the Consecutive Ones Property (COP), and to characterize matrices for which there is a permutation of the rows such that the columns are all sorted in ascending order. We also present a characterization of set systems which have a feasible interval assignment.