FPT algorithms for consecutive ones submatrix problems

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. We consider the parameterized complexity of d-COS-R (Consecutive Ones Submatrix by Row deletions) problem [8]: Given a matrix M and a positive integer d, decide whether there exists a set of at most d rows of M whose deletion results in a matrix with the COP. The closely related Interval Deletion problem has recently been shown to be FPT [5]. In this work, we describe a recursive depth-bounded search tree algorithm in which the problems at the leaf-level of the recursion tree are solved as instances of Interval Deletion. Therefore, we show that d-COS-R is fixed-parameter tractable and has the current best run-time of O*(10d), which is associated with the Interval Deletion problem. We then consider a closely related optimization problem, called Min-ICPIA, and prove that it is computationally equivalent to the Vertex Cover problem. © 2013 Springer International Publishing.