An optimization problem exists in the context of local area network security. The network provides a number of physical or logical "channels", each carrying a set of levels or compartments of information. A channel is accessible to users cleared for all the levels it carries. The problem is to assign the set of levels to be carried by each channel so as to minimize the total number of channels, under the constraint that each pair of users with a level in common can communicate over some channel. This problem was found to be equivalent to a known NP-complete problem, the set basis problem.The main result is an approximate algorithm that runs in polynomial time and finds one solution. It has succeeded in finding an optimal solution in all of the test cases small enough to confirm the optimality independently.