Graph planarization employing a harmony theory artificial neural network

An Artificial Neural Network (ANN) which is based on the principles of Harmony Theory (HT) is proposed for solving the graph planarization problem. Both aspects of the problem are tackled: finding an optimally planarized graph (that contains the minimum number of crossings); and determining a maximal planar subgraph of the original graph (that contains no crossings). The HT ANN is transparent (simple to encode and understand) and accurate (a correct solution of the planarization problem is always produced). Furthermore, it is versatile, since the aspect of the solution (optimally planarized graph or maximally planar subgraph) depends solely upon the flow of activation within the HT ANN and, more specifically, on the relative arrangement of its two layers of nodes.