Efficient Algorithms for Finding Tucker Patterns
Cedric Chauve, Tamon Stephen, Maria Tamayo

TL;DR
This paper presents linear-time algorithms for detecting Tucker patterns in binary matrices that lack the Consecutive Ones Property, enabling efficient certification and enumeration of these forbidden submatrices.
Contribution
It introduces a linear-time algorithm for finding Tucker patterns and an output-sensitive method for enumerating all such patterns in non-C1P matrices.
Findings
Linear-time algorithm for Tucker pattern detection
Output-sensitive enumeration of Tucker patterns
Efficient certification of non-C1P matrices
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 This paper had been withdrawn due to some missing cases in Algorithms 2 and 3.
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Graph Theory Research · Genome Rearrangement Algorithms
