Consecutive ones property testing: cut or swap

Let C be a finite set of $N elements and R = {R_1,R_2, ..,R_m} a family of M subsets of C. The family R verifies the consecutive ones property if there exists a permutation P of C such that each R_i in R is an interval of P. There already exist several algorithms to test this property in sum_{i=1}^m |R_i| time, all being involved. We present a simpler algorithm, based on a new partitioning scheme.