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A Comparison of Steiner Tree Relaxations

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45206

Polzin,  Tobias
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Zitation

Polzin, T., & Vahdati Daneshmand, S. (2001). A Comparison of Steiner Tree Relaxations. Discrete Applied Mathematics, 112, 241-261.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-3158-8
Zusammenfassung
There are many (mixed) integer programming formulations of the Steiner problem in networks. The corresponding linear programming relaxations are of great interest particularly, but not exclusively, for computing lower bounds; but not much has been known about the relative quality of these relaxations. We compare all classical and some new relaxations from a theoretical point of view with respect to their optimal values. Among other things, we prove that the optimal value of a flow-class relaxation (e.g. the multicommodity flow or the dicut relaxation) cannot be worse than the optimal value of a tree-class relaxation (e.g. degree-constrained spanning tree relaxation) and that the ratio of the corresponding optimal values can be arbitrarily large. Furthermore, we present a new flow based relaxation, which is to the authors' knowledge the strongest linear relaxation of polynomial size for the Steiner problem in networks.