A novel neural network method for shortest path tree computation
Shortest path tree (SPT) computation is a critical issue in many real world problems, such as routing in networks. It is also a constrained optimization problem, which has been studied by many authors in recent years. Typically, it is solved by heuristic algorithms, such as the famous Dijkstra's algorithm, which can quickly provide a good solution in most instances. However, with the scale of problem increasing, these methods are inefficient and may consume a considerable amount of CPU time. Neural networks, which are massively parallel models, can solve this question easily. This paper presents an efficient modified continued pulse coupled neural network (MCPCNN) model for SPT computation in a large scale instance. The proposed model is topologically organized with only local lateral connections among neurons. The start neuron fires first, and then the firing event spreads out through the lateral connections among the neurons, like the propagation of a wave. Each neuron records its parent, that is, the neighbor which caused it to fire. It proves that the generated wave in the network spreads outward with travel times proportional to the connection weight between neurons. Thus, the generated path is always the global optimal shortest path from the source to all destinations. The proposed model is also applied to generate SPTs for a real given graph step by step. The effectiveness and efficiency of the proposed approach is demonstrated through simulation and comparison studies.
neural networks shortest path tree wave neural dynamics spiking