MNDB is clearly in NP since it is equivalent to a special case of MIS.
Finally we use Lemma 2.1 to relate the independent set problem on a graph in XP, to the MNDB problem.
Together, these steps transform the independent set problem on the cubic planar graph to an independent set problem on a graph in XP, and we can then conclude the NP-completeness of the MNDB problem using Lemma 2.1.
By Lemma 2.1, the independent set problem on a graph in XT is equivalent to a MNDB problem in a matrix, thus concluding our proof.
Problem MNDB is NP-complete for m x n blocks for m, n [greater than or equal to] 2.
This problem is equivalent to MNDB for square dense blocks.
We begin by presenting a simple linear time 1/2-approximation to the MNDB problem with 2 x 2 blocks which can be generalized for all [sigma]-substructures we present.