Approximation algorithms for the consecutive ones submatrix problem on sparse matrices

Authors:
Jinsong Tan;Louxin Zhang
Affiliations:
Department of Mathematics, National University of Singapore, Singapore;Department of Mathematics, National University of Singapore, Singapore
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

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 proves that the COS problem remains NP-hard for i) (2, 3)-matrices with at most two 1's in each column and at most three 1's in each row and for ii) (3, 2)-matrices with at most three 1's in each column and at most two 1's in each row This solves an open problem posed in a recent paper of Hajiaghayi and Ganjali [12] We further prove that the COS problem is 0.8-approximatable for (2, 3)-matrices and 0.5-approximatable for the matrices in which each column contains at most two 1's and for (3, 2)-matrices.