A Comparison of Steiner Tree Relaxations

Polzin, Tobias ; Vahdati Daneshmand, Siavash

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URL: http://ub-madoc.bib.uni-mannheim.de/1747
URN: urn:nbn:de:bsz:180-madoc-17477
Document Type: Working paper
Year of publication: 1998
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Subject headings (SWD): Steiner-Problem , Relaxation , Untere Schranke
Keywords (English): Steiner problem , relaxation , lower bound
Abstract: 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 ab out 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 flowclass 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.
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