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Mathematical Programming

, Volume 98, Issue 1–3, pp 177–199 | Cite as

Facets of the independent set polytope

  • Todd Easton
  • Kevin Hooker
  • Eva K. LeeEmail author
Article

Abstract.

Theoretical results pertaining to the independent set polytope P ISP =conv{x{0,1} n :Axb} are presented. A conflict hypergraph is constructed based on the set of dependent sets which facilitates the examination of the facial structure of P ISP . Necessary and sufficient conditions are provided for every nontrivial 0-1 facet-defining inequalities of P ISP in terms of hypercliques. The relationship of hypercliques and some classes of knapsack facet-defining inequalities are briefly discussed. The notion of lifting is extended to the conflict hypergraph setting to obtain strong valid inequalities, and back-lifting is introduced to strengthen cut coefficients. Preliminary computational results are presented to illustrate the usefulness of the theoretical findings.

Keywords

independent set polytope conflict hypergraph hyperclique facet integer programming graph theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.School of Industrial and Manufacturing Systems EngineeringKansas State UniversityManhattanKansas
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaGeorgia
  3. 3.Department of Radiation OncologyEmory University School of MedicineAtlantaGeorgia

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