Abstract
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.
Similar content being viewed by others
References
Smolensky P. Information processing in dynamical systems: foundations of harmony theory. In: Rumelhart DE, McClelland JL (Eds.) Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol 1. MIT Press, Cambridge, MA, 1986, pp. 184–281
Takefuji Y, Lin CW, Lee KC. A parallel algorithm for estimating the secondary structure in ribonucleic acids. Biol Cybern 1990; 63: 337–340
Jayakumar R, Thulasiraman K, Swamy MNS.O(n 2) algorithms for graph planarization. IEEE Trans CAD 1989; 8: 257–267
Takefuji T, Lee KC. A near-optimum parallel planarisation algorithm. Science 1989; 245: 1221–1223
Cimikowski R, Shope P. A neural-network algorithm for a graph layout problem. IEEE Trans Neural Networks 1996; 7: 341–345
Hopfield JJ. Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci 1985; 79: 2554–2558
Hinton GE, Sejnowski TJ. Learning and relearning in Boltzmann machines. In: Rumelhart DE, McClelland JL (Eds.) Parallel Distributed Processing: Explorations in the Microstracture of Cognition. Vol 1. MIT Press, Cambridge, MA, 1986, pp. 282–317
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tambouratzis, T. Graph planarization employing a harmony theory artificial neural network. Neural Comput & Applic 6, 116–124 (1997). https://doi.org/10.1007/BF01414008
Issue Date:
DOI: https://doi.org/10.1007/BF01414008