Before revision:  Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users . The proposed solution is based on continuous relaxation, which usually only leads to heuristic or approximate solutions, but the rich structure in our problem renders it an exception. By observing the special structure of a three-dimensional assignment problem derived from the original problem, we show that the obtained solution is not only optimal, but also computationally efficient through judicious choices of the optimization trajectory .
After revision:  Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users .