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Barzilai-Borwein Method in Graph Drawing Algorithm Based on Kamada-Kawai Algorithm
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SYSNO ASEP 0472759 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Barzilai-Borwein Method in Graph Drawing Algorithm Based on Kamada-Kawai Algorithm Author(s) Hasal, Martin (UGN-S)
Pospíšil, L. (CZ)
Nowakova, J. (CZ)Number of authors 3 Article number 360005 Source Title International Conference of Numerical Analysis and Applied Mathematics 2015 (ICNAAM 2015). - New York : AIP Publishing, 2016 / Simos T. ; Tsitouras C. - ISSN 0094-243X - ISBN 978-0-7354-1392-4 Number of pages 4 s. Publication form Online - E Action ICNAAM 2015 - International Conference on Numerical Analysis and Applied Mathematics Event date 23.09.2015 - 29.09.2015 VEvent location Rhodos Country GR - Greece Event type EUR Language eng - English Country US - United States Keywords undirected graphs ; Kamada-Kawai algorithm ; Barzilai-Borwein method Subject RIV BA - General Mathematics Institutional support UGN-S - RVO:68145535 UT WOS 000380803300364 EID SCOPUS 84984577793 DOI 10.1063/1.4952138 Annotation Extension of Kamada-Kawai algorithm, which was designed for calculating layouts of simple undirected graphs, is presented in this paper. Graphs drawn by Kamada-Kawai algorithm exhibit symmetries, tend to produce aesthetically pleasing and crossing-free layouts for planar graphs. Minimization of Kamada-Kawai algorithm is based on Newton-Raphson method, which needs Hessian matrix of second derivatives of minimized node. Disadvantage of Kamada-Kawai embedder algorithm is computational requirements. This is caused by searching of minimal potential energy of the whole system, which is minimized node by node. The node with highest energy is minimized against all nodes till the local equilibrium state is reached. In this paper with Barzilai-Borwein (BB) minimization algorithm, which needs only gradient for minimum searching, instead of Newton-Raphson method, is worked. It significantly improves the computational time and requirements. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2017 Electronic address http://aip.scitation.org/doi/pdf/10.1063/1.4952138
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