Primal and dual assignment networks

This paper presents two recurrent neural networks for solving the assignment problem. Simplifying the architecture of a recurrent neural network based on the primal assignment problem, the first recurrent neural network, called the primal assignment network, has less complex connectivity than its predecessor. The second recurrent neural network, called the dual assignment network, based on the dual assignment problem, is even simpler in architecture than the primal assignment network. The primal and dual assignment networks are guaranteed to make optimal assignment. The applications of the primal and dual assignment networks for sorting and shortest-path routing are discussed. The performance and operating characteristics of the dual assignment network are demonstrated by means of illustrative examples.