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dc.contributor.authorChen, Kennethen_US
dc.date.accessioned2011-09-22T17:48:18Z
dc.date.available2011-09-22T17:48:18Z
dc.date.issued2011-06-15en_US
dc.identifier.urihttp://hdl.handle.net/1853/41133
dc.description.abstractIn 2003, Gomory and Johnson gave two different three-slope T-space facet constructions, both of which shared a slope with the corresponding Gomory mixed-integer cut. We give a new three-slope facet which is independent of the GMIC and also give a four-slope T-space facet construction, which to our knowledge, is the first four-slope construction. We describe an enumerative framework for the discovery of T-space facets. Using an algorithm by Harvey for computing integer hulls in the plane, we give a heuristic for quickly computing lattice-free triangles. Given two rows of the tableau, we derive how to exactly calculate lattice-free triangles and quadrilaterals in the plane which can be used to derive facet-defining inequalities of the integer hull. We then present computational results using these derivations where non-basic integer variables are strengthened using Balas-Jeroslow lifting.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectLattice-free setsen_US
dc.subjectT-space facetsen_US
dc.subjectMixed-integer programmingen_US
dc.subject.lcshInteger programming
dc.titleTopics in group methods for integer programmingen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Cook, William J.; Committee Member: Johnson, Ellis L.; Committee Member: Nemhauser, George L.; Committee Member: Parker, R. Gary; Committee Member: Tetali, Prasaden_US


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