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  <doc>
    <id>4223</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-08-30</completedDate>
    <publishedDate>2013-08-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">HUHFA: A Framework for Facet Classification</title>
    <abstract language="eng">Usually complete linear descriptions of polytopes consist of&#13;
an enormous number of facet-defining inequalities already&#13;
for very small problem sizes. In this paper, we describe a method&#13;
for dividing the inequalities into equivalence classes without resorting to a normal form. Within each&#13;
class, facets are related by certain symmetries and it is sufficient&#13;
to list one representative of each class to give a complete&#13;
picture of the structural properties of a polytope. We propose an algorithm&#13;
for the classification and illustrate its efficiency on a broad range of combinatorial optimization problems including the Traveling Salesman and the Linear Ordering Problem.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42230</identifier>
    <author>Olga Heismann</author>
    <submitter>Olga Heismann</submitter>
    <author>Achim Hildenbrandt</author>
    <author>Francesco Silvestri</author>
    <author>Gerhard Reinelt</author>
    <author>Ralf Borndörfer</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-45</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>facet classification</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>symmetry</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral structure</value>
    </subject>
    <collection role="msc" number="52B15">Symmetry properties of polytopes</collection>
    <collection role="msc" number="68-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MATHEON-B22">MATHEON-B22</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4223/ZR 13-45.pdf</file>
  </doc>
</export-example>
