Finding minimum Tucker submatrices
Abstract
A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. These matrices are used for DNA physical mapping and ancestral genome reconstruction in computational biology on the other hand they represents a class of convex bipartite graphs and are of interest of algorithm graph theory researchers. Tucker gave a forbidden submartices characterization of matrices that have C1P property in 1972. Booth and Lucker (1976) gave a first linear time recognition algorithm for matrices with C1P property and then in 2002, Habib, et al. gave a simpler linear time recognition algorithm. There has been substantial amount of works on efficiently finding minimum size forbidden submatrix. Our algorithm is at least times faster than the existing algorithm where is the number of columns of the input matrix.
Cite
@article{arxiv.1401.4739,
title = {Finding minimum Tucker submatrices},
author = {Jan Manuch and Arash Rafiey},
journal= {arXiv preprint arXiv:1401.4739},
year = {2014}
}