Packing Steiner Trees: Polyhedral Investigations

Grötschel M, Martin A, Weismantel R (1996)

Publication Language: English

Publication Type: Journal article

Publication year: 1996

Journal

Mathematical Programming Springer Verlag (Germany)

Book Volume: 72

Pages Range: 101 - 123

Abstract

LetG=(V, E) be a graph andT⊆V be a node set. We call an edge setS a Steiner tree forT ifS connects all pairs of nodes inT. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graphG=(V, E) with edge weightswe, edge capacitiesce,e∈E, and node setT1,…,TN, find edge setsS1,…,SN such that eachSk is a Steiner tree forTk, at mostce of these edge sets use edgee for eache∈E, and the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from a routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the Steiner tree packing problem from a polyhedral point of view and define an associated polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facet-defining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of so-called joint inequalities that are valid and facet-defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper (in this issue).

Authors with CRIS profile

Alexander Martin Economics - Discrete Optimization - Mathematics (EDOM)

Involved external institutions

Konrad-Zuse-Zentrum für Informationstechnik / Zuse Institute Berlin (ZIB) DE Germany (DE)

How to cite

APA:

Grötschel, M., Martin, A., & Weismantel, R. (1996). Packing Steiner Trees: Polyhedral Investigations. Mathematical Programming, 72, 101 - 123.

MLA:

Grötschel, Martin, Alexander Martin, and Robert Weismantel. "Packing Steiner Trees: Polyhedral Investigations." Mathematical Programming 72 (1996): 101 - 123.

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