A Faster Algorithm for 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. Algorithmic issues of the C1P are central in computational molecular biology, in particular for physical mapping and ancestral genome reconstruction. In 1972, Tucker gave a characterization of matrices that have the C1P by a set of forbidden submatrices, and a substantial amount of research has been devoted to the problem of efficiently finding such a minimum size forbidden submatrix. This paper presents a new O(Δ3m2(mΔ + n3)) time algorithm for this particular task for a m×n binary matrix with at most Δ 1-entries per row, thereby improving the O(Δ3m2(mn + n3)) time algorithm of Dom et al. [17].