Strong Formulations for Network Design Problems with Connectivity Requirements
Name
OR-332-99.pdf
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3.06 MB
Format
Adobe PDF
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7318957a204dd45054d8838b264e52ad
Author(s)
Magnanti, Thomas L.
Raghavant, S.
Date Issued
April 1999
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 332-99
Abstract
The network design problem with connectivity requirements (NDC) models a wide variety of celebrated combinatorial optimization problems including the minimum spanning tree, Steiner tree, and survivable network design problems. We develop strong formulations for two versions of the edge-connectivity NDC problem: unitary problems requiring connected network designs, and nonunitary problems permitting non-connected networks as solutions. We (i) present a new directed formulation for the unitary NDC problem that is stronger than a natural undirected formulation, (ii) project out several classes of valid inequalities-partition inequalities, odd-hole inequalities, and combinatorial design inequalities-that generalize known classes of valid inequalities for the Steiner tree problem to the unitary NDC problem, and (iii) show how to strengthen and direct nonunitary problems. Our results provide a unifying framework for strengthening formulations for NDC problems, and demonstrate the strength and power of flow-based formulations for network design problems with connectivity requirements.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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