A CONNECTIONIST APPROACH TO VERTEX COVERING PROBLEMS

Abstract

This paper describes a connectionist approach to solving computationally difficult minimum vertex covering problems. This approach uses the graph representing the vertex covering problem as the connectionist network without any modifications (nodes of the connectionist network represent vertices and links represent edges of the given graph). The activation rule governing node behavior is derived by breaking down the global constraints on a solution into local constraints on individual nodes. The resulting model uses a competitive activation mechanism to carry out the computation where vertices compete not by explicit inhibitory links but through common resources (edges). Convergence and other properties of this model are formally established by introducing a monotonically non-increasing global energy function. Simulation results show that this model yields very high accuracy, significantly outperforming a well-known sequential approximation algorithm.