English

Efficient Algorithms for Finding Tucker Patterns

Data Structures and Algorithms 2012-07-03 v2 Discrete Mathematics

Abstract

The Consecutive Ones Property is an important notion for binary matrices, both from a theoretical and applied point of view. Tucker gave in 1972 a characterization of matrices that do not satisfy the Consecutive Ones Property in terms of forbidden submatrices, the Tucker patterns. We describe here a linear time algorithm to find a Tucker pattern in a non-C1P binary matrix, which allows to extract in linear time a certificate for the non-C1P. We also describe an output-sensitive algorithm to enumerate all Tucker patterns of a non-C1P binary matrix. This paper had been withdrawn due to some missing cases in Algorithms 2 and 3.

Keywords

Cite

@article{arxiv.1206.1837,
  title  = {Efficient Algorithms for Finding Tucker Patterns},
  author = {Cedric Chauve and Tamon Stephen and Maria Tamayo},
  journal= {arXiv preprint arXiv:1206.1837},
  year   = {2012}
}

Comments

15 pages. Preliminary version This paper had been withdrawn due to some missing cases in Algorithms 2 and 3

R2 v1 2026-06-21T21:16:30.710Z