Neural networks for optimization problems in graph theory

This paper presents a novel technique to map the minimum vertex cover and related problems onto the Hopfield neural networks. The proposed approach can be used to find near-optimum solutions for these problems in parallel, and particularly the network algorithm always yields minimal vertex covers. Further, the relationships between Boolean equations and arithmetic functions are presented. Based on these relationships, other NP-complete problems in graph theory can also be solved by neural networks. Extensive simulation was performed and the experimental results demonstrate that the network algorithm outperforms the well-known greedy algorithm for the vertex cover problem