A Modified Hopfield Neural Network for the Minimum Vertex Cover Problem

Abstract

The minimum vertex cover(MVC) problem is a classic graph optimization problem. It is well known that it is NP-Complete problem. In this paper, a modified Hopfield neural network is presented for the minimum vertex cover problem. In the modified Hopfield neural network, a correction term is introduced into the motion equation. With this correction term, the modified Hopfield network can find optimal or near-optimal solutions for the minimum vertex cover problem in higher probability. Extensive simulations are performed, and the results show that the modified Hopfield neural network works much better than other existing algorithms for this problem on both random graphs and DIMACS benchmark graphs.