Optimal patchings for consecutive ones matrices

Abstract

We study a variant of the weighted consecutive ones property problem. Here, a 0/1-matrix is given with a cost associated to each of its entries and one has to find a minimum cost set of zero entries to be turned to ones in order to make the matrix have the consecutive ones property for rows. We investigate polyhedral and combinatorial properties of the problem and we exploit them in a branch-and-cut algorithm. In particular, we devise preprocessing rules and investigate variants of “local cuts”. We test the resulting algorithm on a number of instances, and we report on these computational experiments.