Abstract
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 [1976] 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.
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References
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.
N. Korte and R. H. Möhring, An Incremental Linear-Time Algorithm for Recognizing Interval Graphs, SIAM J. Comput. 18, (1989), 68–81.
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© 1992 Springer-Verlag Berlin Heidelberg
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Hsu, WL. (1992). A simple test for the consecutive ones property. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_98
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DOI: https://doi.org/10.1007/3-540-56279-6_98
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