<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>1061</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-02-20</completedDate>
    <publishedDate>2008-02-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the cardinality constrained matroid polytope</title>
    <abstract language="eng">Edmonds showed that the so-called rank inequalities and the nonnegativity constraints provide a complete linear description of the matroid polytope. By essentially adding Grötschel's cardinality forcing inequalities, we obtain a complete linear description of the cardinality constrained matroid polytope which is the convex hull of the incidence vectors of those independent sets that have a feasible cardinality. Moreover, we show how the separation problem for the cardinality forcing inequalities can be reduced to that for the rank inequalities. We also give necessary and sufficient conditions for a cardinality forcing inequality to be facet defining.</abstract>
    <identifier type="serial">08-08</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1090</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10614</identifier>
    <author>Rüdiger Stephan</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-08</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Matroid-Polytop</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Kardinalitätsbeschränkung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Separationsalgorithmus</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Matroid Polytope</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cardinality constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Separation algorithm</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="05B35">Matroids, geometric lattices [See also 52B40, 90C27]</collection>
    <collection role="msc" number="52B40">Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="CCCO">CCCO</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1061/MatroidCard_ZIB.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1061/MatroidCard_ZIB.ps</file>
  </doc>
</export-example>
