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# Network Flow Models for Designing Diameter-Constrained Minimum Spanning and Steiner Trees

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 dc.contributor.author Gouveia, Luis en_US dc.contributor.author Magnanti, Thomas L. en_US dc.date.accessioned 2004-05-28T19:33:01Z dc.date.available 2004-05-28T19:33:01Z dc.date.issued 2001-08 en_US dc.identifier.uri http://hdl.handle.net/1721.1/5310 dc.description.abstract The 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.extent 2739071 bytes dc.format.mimetype application/pdf dc.language.iso en_US en_US dc.publisher Massachusetts Institute of Technology, Operations Research Center en_US dc.relation.ispartofseries Operations Research Center Working Paper;OR 359-01 en_US dc.subject Spanning Trees, Steiner Trees, Diameter Constraints, Multicommodity Flow Models, Hop-Indexed Models. en_US dc.title Network Flow Models for Designing Diameter-Constrained Minimum Spanning and Steiner Trees en_US dc.type Working Paper en_US
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