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 ones 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 quite complicated and the linear time amortized analysis is also rather involved. We developed an off-line linear time test for the consecutive ones property without using PQ-trees and the corresponding template matching, which is considerably simpler. A simplification of the consecutive ones test will immediately simplify algorithms (and computer codes) for interval graph and planar graph recognition. Our approach is based on a decomposition technique that separates the rows into prime subsets, each of which admits essentially a unique column ordering that realizes the consecutive ones property. The success of this approach is based on finding a good "row ordering" to be tested iteratively.