Approximation and fixed-parameter algorithms for consecutive ones submatrix problems

Approximability and Parameterized Complexity of Consecutive Ones Submatrix Problems

We develop a refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the problem to find a maximum-size submatrix of a 0/1-matrix such that the submatrix has the C1P. Moreover, we achieve a proble...

Fixed-Parameter Tractability of the Simultaneous Consecutive Ones Submatrix & Editing Problems

A binary matrix has the consecutive ones property (C1P ) for rows (columns) if there is a permutation of its columns (rows) that arranges the ones consecutively in all the rows (columns). A binary matrix has the simultaneous consecutive ones property (SC1P ) if it has both the C1P for rows and columns. We consider the following two categories of problems: Simultaneous Consecutive Ones Submatrix...

The Search for Consecutive Ones Submatrices: Faster and More General

Finding for a given 0/1-matrix a maximum-size submatrix that fulfills the Consecutive Ones Property is generally an NP-hard problem. Based on previous work, we present improved approximation and fixed-parameter algorithms for obtaining such submatrices by a minimum number of column deletions. Moreover, we show how to extend these results to the non-symmetrical case where instead of column delet...

Approximation Algorithms for the Consecutive Ones Submatrix Problem on Sparse Matrices

A 0-1 matrix has the Consecutive Ones Property (C1P) if there is a permutation of its columns that leaves the 1’s consecutive in each row. The Consecutive Ones Submatrix (COS) problem is, given a 0-1 matrix A, to find the largest number of columns of A that form a submatrix with the C1P property. Such a problem has potential applications in physical mapping with hybridization data. This paper p...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems