A greedy algorithm is usually attractive due to its simplicity.
In [#!greedy-setcover-johnson!#,#!greedy-setcover-lovasz!#], Johnson and
Lovász introduced a greedy algorithm for the set cover problem
with an 
approximation ratio. The basic greedy attribute of
the algorithm is to select a set at every step that contains the
maximum number of uncovered elements. For the backup problem variant,
we extend the algorithm by treating any node that has not satisfied
the constraints of (5.2) and
(5.3) as equally uncovered. At each step, we
select a set that has the largest number of remaining uncovered nodes
and repeat till there are no more uncovered nodes.