A COMPETITIVE ACTIVATION NEURAL NETWORK MODEL FOR THE WEIGHTED MINIMUM VERTEX COVERING

We give a generalization of a neural network model originally developed to solve the minimum cardinality vertex covering problem, in order to solve the weighted version of the problem. The model is governed by a modified activation rule and we show that it has some important properties, namely convergence and irredundant covers at stable states. We present experimental results that confirm the effectiveness of the model.

LEARNING ACTIVATION RULES RATHER THAN CONNECTION WEIGHTS

In the construction of neural networks involving associative recall, information is sometimes best encoded with a local representation. Moreover, a priori knowledge can lead to a natural selection of connection weights for these networks. With predetermined and fixed weights, standard learning algorithms that work by altering connection strengths are unable to train such networks. To address this problem, this paper derives a supervised learning rule based on gradient descent, where connection weights are fixed and a network is trained by changing the activation rule. It incorporates both traditional and competitive activation mechanisms, the latter being an efficient method for instilling competition in a network. The learning rule has been implemented, and the results from several test networks demonstrate that it works effectively.

A CONNECTIONIST APPROACH TO VERTEX COVERING PROBLEMS

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.