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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2382

Title: An improved neural network model for the two-page crossing number problem
Authors: He, H.
Sykora, Ondrej
Mäkinen, E.
Keywords: 2-page crossing number
Hopfield model
Energy function
Motion equation
Learning algorithms
Issue Date: 2006
Publisher: © IEEE Computational Intelligence Society
Citation: HE, H., SÝKORA, O. and MÄKINEN, E., 2006. An improved neural network model for the two-page crossing number problem. IEEE Transactions on Neural Neworks, 17 (6), pp.1642-1646
Abstract: The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as half-circles either above or below the line. Such drawings are called 2-page book drawings. The smallest number of crossings over all 2-page drawings of a graph G is called the 2-page crossing number of G. Cimikowski and Shope have solved the 2-page crossing number problem for an n-vertex and m-edge graph by using a Hopfield network with 2m neurons. We present here an improved Hopfield modelwith m neurons. The new model achieves much better performance in the quality of solutions and is more efficient than the model of Cimikowski and Shope for all graphs tested. The parallel time complexity of the algorithm, without considering the crossing number calculations, is O(m), for the new Hopfield model with m processors clearly outperforming the previous algorithm.
Description: This article was published in the journal, IEEE Transactions on Neural Networks [© IEEE]. It is also available at: http://ieeexplore.ieee.org/ Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
URI: https://dspace.lboro.ac.uk/2134/2382
ISBN: 1045-9227
Appears in Collections:Published Articles (Computer Science)

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