An Efficient Neural Algorithm for Two-layer Planarization Problem in Graph Drawing

Abstract

A neural algorithm for the two-layer planarization problem using a gradient ascent learning of the Hopfield network is presented. This algorithm which is designed to embed a two-layer graph on a plane, uses the Hopfield network to get a near-maximal two-layer planar subgraph, and increases the energy by modifying the weights and the thresholds in gradient ascent direction to help the network escape from the state of near-maximal two-layer planar subgraph to the state of the maximal two-layer planar subgraph. The experimental results show that the proposed algorithm generates much better solutions than traditional Hopfield network and simulated annealing.