Generalizations of the Consecutive Ones Property and Related NP-Complete Problems 1

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.