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Spatial graph embeddings and coupler curves - source code and results

Legerský, Jan; Bartzos, Evangelos


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    "creators": [
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        "affiliation": "Research Institute for Symbolic Computation, \\\\ Johannes Kepler University Linz, Austria", 
        "name": "Legersk\u00fd, Jan", 
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        "affiliation": "Department of Informatics and Telecommunications, National Kapodistrian University of Athens, and ATHENA Research Center", 
        "name": "Bartzos, Evangelos"
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    "description": "<p>This is supplementary material for the paper&nbsp;<em>On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs</em> accepted to ISSAC 2018, see&nbsp;<a href=\"https://arxiv.org/abs/1802.05860\">preprint</a>&nbsp;and&nbsp;<a href=\"http://jan.legersky.cz/project/spatialgraphembeddings/\">project website</a>&nbsp;for details. It includes source code and results.</p>\n\n<p><strong>Construction of Geiringer graphs</strong></p>\n\n<p>Sage and Matlab code for construction of Geiringer graphs using Henneberg steps.</p>\n\n<p><strong>Computation of mixed volume and complex solutions</strong></p>\n\n<p>Functions that&nbsp;compute the mixed volume and the (complex) embeddings of a given graph using different algebraic formulations.</p>\n\n<p><strong>Coupler curve visualization and sampling</strong></p>\n\n<p>Implementation of&nbsp;our&nbsp;method for obtaining edge lengths of a Geiringer&nbsp;graph with many real spatial embeddings.<br>\nVisualization of coupler curves of the 7-vertex Geiringer graph with the maximal number of&nbsp;real embeddings (G48).</p>\n\n<p><strong>Maple parametric_search</strong></p>\n\n<p>Maple worksheet illustrating a method to improve number of real embeddings of G48 using RootFinding[Parametric] subpackage.</p>\n\n<p><strong>Results</strong></p>\n\n<p>Full list of Geiringer graphs up to 8 vertices.<br>\nEdge lengths of graphs obtained by our method that maximizes number of real embeddings.&nbsp;<br>\nMaple script verifying the results.</p>", 
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      "rigid graph", 
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