Title:
Facets of conflict hypergraphs

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dc.contributor.advisor Lee, Eva K.
dc.contributor.author Maheshwary, Siddhartha en_US
dc.contributor.committeeMember Barnes, Earl R.
dc.contributor.committeeMember Johnson, Ellis L.
dc.contributor.committeeMember Parker, R. Gary
dc.contributor.committeeMember Wu, D. J.
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2009-01-22T15:52:27Z
dc.date.available 2009-01-22T15:52:27Z
dc.date.issued 2008-08-25 en_US
dc.description.abstract We study the facial structure of the independent set polytope using the concept of conflict hypergraphs. A conflict hypergraph is a hypergraph whose vertices correspond to the binary variables, and edges correspond to covers in the constraint matrix of the independent set polytope. Various structures such as cliques, odd holes, odd anti-holes, webs and anti-webs are identified on the conflict hypergraph. These hypergraph structures are shown to be generalization of traditional graph structures. Valid inequalities are derived from these hypergraph structures, and the facet defining conditions are studied. Chvatal-Gomory ranks are derived for odd hole and clique inequalities. To test the hypergraph cuts, we conduct computational experiments on market-share (also referred to as market-split) problems. These instances consist of 100% dense multiple-knapsack constraints. They are small in size but are extremely hard to solve by traditional means. Their difficult nature is attributed mainly to the dense and symmetrical structure. We employ a special branching strategy in combination with the hypergraph inequalities to solve many of the particularly difficult instances. Results are reported for serial as well as parallel implementations. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/26635
dc.publisher Georgia Institute of Technology en_US
dc.subject Facet en_US
dc.subject Valid inequality en_US
dc.subject Conflict hypergraph en_US
dc.subject Conflict graph en_US
dc.subject Independent set polytope en_US
dc.subject Independent set problem en_US
dc.subject Combinatorial optimization en_US
dc.subject Integer programming en_US
dc.subject Market split en_US
dc.subject Market share en_US
dc.subject Parallel computing en_US
dc.subject.lcsh Hypergraphs
dc.title Facets of conflict hypergraphs en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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