Note that the maximum independent set and minimum vertex cover problems are complementary.

Lemma 10 For any set L of n lines, a maximum independent set of the corresponding [H.

A maximum independent set (mis) is a maximum cardinality subset of V such that there is no edge between any two vertices of it.

In particular, for any two members of a minimum connected dominating set (mcds), there are at most seven independent vertices in maximum independent set, that is |mis| [less than or equal to] 3.

We show that the maximum nonoverlapping dense blocks problem is NP-complete by a reduction from the maximum independent set problem on cubic planar graphs.

In Section 2, we define the problem formally and investigate its relation to the maximum independent set problem.

A solution to the NP-hard maximum independent set problem is an independent set of maximum cardinality.

Additional Key Words and Phrases: Combinatorial optimization, Fortran subroutines, GRASP, local search, maximum clique, maximum independent set

j] does not belong to E, and the maximum independent set problem (IS) is to find a maximum size independent set.

Tau](G)) and the corresponding maximum independent set [S.

In the MAXIMUM Independent Set problem (MIS), the input is a graph and the task is to find a largest independent set in this graph.

It is known that a maximum independent set of a graph on n vertices can be computed in O([1.