Neural network solution to the link scheduling problem using convex relaxation

The convex relaxation method for the neural network solution of combinatorial optimization problems is presented. The method is applied to the NP-complete problem of finding a minimum-length link schedule in a multihop radio network with given link demands. The link scheduling problem can be reduced to the graph coloring problem, which can in turn be reduced to the maximum-independent-set problem. Simulations show that, for the latter problem, convex relaxation computes significantly better solutions than neural network methods based on gradient descent and produces solutions comparable to those obtained with the Hammer greedy serial algorithm. A modified version of mean field annealing (MFA) is also presented and shown to have the same time-varying energy function as that for convex relaxation