The simultaneous consecutive ones problem

Abstract

The standard consecutive ones problem is concerned with permuting the columns of a 0/1-matrix in such a way that in every row all 1-entries occur consecutively. In this paper we study this problem with the additional requirement that also in every column the 1-entries have to be consecutive. To achieve this column permutations have to be allowed as well. We show that the weighted simultaneous consecutive ones problem is NP-hard and consider two special cases with fixed row and column permutations where one is still NP-hard and the other one turns out to be easy.