d-COS-R is FPT via Interval Deletion

A binary matrix M has the Consecutive Ones Property (COP) if there exists a permutation of columns that arranges the ones consecutively in all the rows. Given a matrix, the d-COS-R problem is to determine if there exists a set of at most d rows whose deletion results in a matrix with COP. We consider the parameterized complexity of this problem with respect to the number d of rows to be deleted as the parameter. The closely related Interval Deletion problem has recently shown to be FPT [22]. In this work, we describe a recursive depth-bounded search tree algorithm in which the problems at the leaf-level are solved as instances of Interval Deletion. The running time of the algorithm is dominated by the running time of Interval Deletion, and therefore we show that d-COS-R is fixedparameter tractable and has a run-time of O∗(10d).