Abstract
A(O,1)-matrix A is said to have the consecutive ones property if its rows can be permuted so that the 1’s appear consecutively in each column. We present four NP-complete problems connected with some generalizations of this notion. These problems concern decomposing the columns of a matrix into two subsets having the consecutive ones property, decomposing the rows into three subsets having the consecutive ones property, finding a subset of rows of maximal size having the consecutive ones property, and finding a permutation of the rows such that the 1’s in any column are contained in a set of k consecutive rows, for a fixed “buffer size” k.
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