PC trees and circular-ones arrangements

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A 0-1 matrix has the consecutive-ones property if its columns can be ordered so that the ones in every row are consecutive. It has the circular-ones property if its columns can be ordered so that, in every row, either the ones or the zeros are consecutive. PQ trees are used for representing all consecutive-ones orderings of the columns of a matrix that have the consecutive-ones property. We give an analogous structure, called a PC tree, for representing all circular-ones orderings of the columns of a matrix that has the circular-ones property. No such representation has been given previously. In contrast to PQ trees, PC trees are unrooted. We obtain a much simpler algorithm for computing PQ trees that those that were previously available, by adding a zero column, x, to a matrix, computing the PC tree, and then picking the PC tree up by x to root it. © 2002 Elsevier Science B.V. All rights reserved.




Hsu, W. L., & McConnell, R. M. (2003). PC trees and circular-ones arrangements. In Theoretical Computer Science (Vol. 296, pp. 99–116). https://doi.org/10.1016/S0304-3975(02)00435-8

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