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Title: A Hopfield neural network model for the outerplanar crossing number problem
Authors: He, Hongmei
Sykora, Ondrej
Keywords: outerplanar crossing number
Hopfield model
energy function
motion equation
learning algorithms
Issue Date: 2006
Publisher: © IAENG
Citation: HE and SÝKORA, 2006. A Hopfield neural network model for the outerplanar crossing number problem. IN: Proceedings of the International MultiConference of Engineers and Computer Scientists 2006, (IMECS '06), June 20 - 22, 2006, Hong Kong
Abstract: In the outerplanar (other alternate concepts are circular or one-page) drawing, one places vertices of a n-vertex m-edge connected graph G along a circle, and the edges are drawn as straight lines. The minimal number of crossings over all outerplanar drawings of the graph G is called the outerplanar (circular, convex, or one-page) crossing number of the graph G. To find a drawing achieving the minimum crossing number is an NP-hard problem. In this work we investigate the outerplanar crossing number problem with a Hopfield neural network model, and improve the convergence of the network by using the Hill Climbing algorithm with local movement. We use two kinds of energy functions, and compare their convergence. We also test a special kind of graphs, complete p-partite graphs. The experimental results show the neural network model can achieve crossing numbers close to the optimal values of the graphs tested.
Description: This is a conference paper
URI: https://dspace.lboro.ac.uk/2134/2379
ISBN: 9889867133
Appears in Collections:Conference Papers and Presentations (Computer Science)

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