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. © 2001 Elsevier Science B.V.
CITATION STYLE
Polzin, T., & Daneshmand, S. V. (2001). A comparison of Steiner tree relaxations. Discrete Applied Mathematics, 112(1–3), 241–261. https://doi.org/10.1016/S0166-218X(00)00318-8
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