A simple test for the consecutive ones property

  • Wen-Lian Hsu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)


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.


Interval Graph Span Forest Column Permutation Prime Matrix Unique Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 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
  2. 2.
    N. Korte and R. H. Möhring, An Incremental Linear-Time Algorithm for Recognizing Interval Graphs, SIAM J. Comput. 18, (1989), 68–81.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Wen-Lian Hsu
    • 1
  1. 1.Institute of Information ScienceAcademia SinicaNankang, TaipeiTaiwan, Republic of China

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