A simple test for the consecutive ones property
A (0,1)-matrix satisfies the consecutive ones property if there exists a column permutation such that the one's in each row of the resulting matrix are consecutive. Booth and Lueker  designed a linear time testing algorithm for this property based on a data structure called “PQ-trees”. This procedure is very complicated and the linear time amortized analysis is also rather involved. We develop an off-line testing algorithm for the consecutive ones property without using PQ-trees. Our approach is based on a decomposition technique which separates the rows into “prime” subsets which admit unique column orderings that realize the consecutive ones property. The success of this approach is based on finding a good “row ordering” to be tested iteratively.
KeywordsInterval Graph Span Forest Column Permutation Prime Matrix Unique Partition
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- 1.K. S. Booth and G. S. Lueker, Testing of the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comptr. Syst. Sci. 13, 3 (1976), 335–379.Google Scholar