ON THE PERFORMANCE GUARANTEE OF NEURAL NETWORKS FOR NP-HARD OPTIMIZATION PROBLEMS

We give polynomial size threshold neural networks and encoding formalisms, which guarantee worst case performance for two hard optimization problems. We show that a massively parallel algorithm based on such neural network models guarantee an approximation ratio, asymptotically equal to DELTA/2 for the maximum independent set problem, where DELTA is the maximum degree of the graph, and equal to 2 for the vertex covering problem. These results on the power of polynomial size threshold neural networks within polynomial number of neural updates provide the first approximation results for neural network models.