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dc.contributor.authorGouveia, Luisen_US
dc.contributor.authorMagnanti, Thomas L.en_US
dc.date.accessioned2004-05-28T19:33:01Z
dc.date.available2004-05-28T19:33:01Z
dc.date.issued2001-08en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/5310
dc.description.abstractThe Diameter-Constrained Minimum Spanning Tree Problem seeks a least cost spanning tree subject to a (diameter) bound imposed on the number of edges in the tree between any node pair. A traditional multicommodity flow model with a commodity for every pair of nodes was unable to solve a 20-node and 100-edge problem after one week of computation. We formulate the problem as a directed tree from a selected central node or a selected central edge. Our model simultaneously finds a central node or a central edge and uses it as the source for the commodities in a directed multicommodity flow model with hop constraints. The new model has been able to solve the 20-node, 100-edge instance to optimality after less than four seconds. We also present model enhancements when the diameter bound is odd (these situations are more difficult). We show that the linear programming relaxation of the best formulations discussed in this paper always give an optimal integer solution for two special, polynomially-solvable cases of the problem. We also examine the Diameter Constrained Minimum Steiner Tree problem. We present computational experience in solving problem instances with up to 100 nodes and 1000 edges. The largest model contains more than 250,000 integer variables and more than 125,000 constraints.en_US
dc.format.extent2739071 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_USen_US
dc.publisherMassachusetts Institute of Technology, Operations Research Centeren_US
dc.relation.ispartofseriesOperations Research Center Working Paper;OR 359-01en_US
dc.subjectSpanning Trees, Steiner Trees, Diameter Constraints, Multicommodity Flow Models, Hop-Indexed Models.en_US
dc.titleNetwork Flow Models for Designing Diameter-Constrained Minimum Spanning and Steiner Treesen_US
dc.typeWorking Paperen_US


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