On a posterior evaluation of a simple greedy method for set packing

We consider an approach for ex post evaluation of approximate solutions obtained by a well known simple greedy method for set packing. A performance bound is derived that is a function of the highest average reward per item over subsets as well as the number of allocated subsets and ground items. This a posterior bound can enable much revelation of optimality when the solution is near optimal. One of the advantages of the ex post analysis is that it does not require computing the optimal solution to the LP relaxation. The ex post bound will not be guaranteed to reveal substantial levels of optimality for all problem instances but can be a useful tool that is complementary to other traditional methods for ex post evaluation for the set packing problem.