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Spatial graph embeddings and coupler curves - source code and results

Legerský, Jan; Bartzos, Evangelos


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  <identifier identifierType="DOI">10.5281/zenodo.1244042</identifier>
  <creators>
    <creator>
      <creatorName>Legerský, Jan</creatorName>
      <givenName>Jan</givenName>
      <familyName>Legerský</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-8122-668X</nameIdentifier>
      <affiliation>Research Institute for Symbolic Computation, \\ Johannes Kepler University Linz, Austria</affiliation>
    </creator>
    <creator>
      <creatorName>Bartzos, Evangelos</creatorName>
      <givenName>Evangelos</givenName>
      <familyName>Bartzos</familyName>
      <affiliation>Department of Informatics and Telecommunications, National Kapodistrian University of Athens, and ATHENA Research Center</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Spatial Graph Embeddings And Coupler Curves - Source Code And Results</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2018</publicationYear>
  <subjects>
    <subject>rigid graph</subject>
    <subject>spatial real embedding</subject>
    <subject>coupler curve</subject>
    <subject>mixed volume</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2018-05-09</date>
  </dates>
  <resourceType resourceTypeGeneral="Software"/>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/1244042</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsSupplementTo">https://arxiv.org/abs/1802.05860</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.1244041</relatedIdentifier>
  </relatedIdentifiers>
  <version>issac18</version>
  <rightsList>
    <rights rightsURI="http://www.opensource.org/licenses/GPL-3.0">GNU General Public License 3.0</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;This is supplementary material for the paper&amp;nbsp;&lt;em&gt;On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs&lt;/em&gt; accepted to ISSAC 2018, see&amp;nbsp;&lt;a href="https://arxiv.org/abs/1802.05860"&gt;preprint&lt;/a&gt;&amp;nbsp;and&amp;nbsp;&lt;a href="http://jan.legersky.cz/project/spatialgraphembeddings/"&gt;project website&lt;/a&gt;&amp;nbsp;for details. It includes source code and results.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Construction of Geiringer graphs&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Sage and Matlab code for construction of Geiringer graphs using Henneberg steps.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Computation of mixed volume and complex solutions&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Functions that&amp;nbsp;compute the mixed volume and the (complex) embeddings of a given graph using different algebraic formulations.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Coupler curve visualization and sampling&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Implementation of&amp;nbsp;our&amp;nbsp;method for obtaining edge lengths of a Geiringer&amp;nbsp;graph with many real spatial embeddings.&lt;br&gt;
Visualization of coupler curves of the 7-vertex Geiringer graph with the maximal number of&amp;nbsp;real embeddings (G48).&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Maple parametric_search&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Maple worksheet illustrating a method to improve number of real embeddings of G48 using RootFinding[Parametric] subpackage.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Results&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Full list of Geiringer graphs up to 8 vertices.&lt;br&gt;
Edge lengths of graphs obtained by our method that maximizes number of real embeddings.&amp;nbsp;&lt;br&gt;
Maple script verifying the results.&lt;/p&gt;</description>
  </descriptions>
</resource>

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