Packing Steiner Trees: Polyhedral Investigations

Journal article


Publication Details

Author(s): Grötschel M, Martin A, Weismantel R
Journal: Mathematical Programming
Publication year: 1996
Volume: 72
Pages range: 101 - 123
ISSN: 0025-5610
Language: English


Abstract


LetG=(V, E) be a graph andTV 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,eE, 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 eacheE, 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).



FAU Authors / FAU Editors

Martin, Alexander Prof. Dr.
Economics - Discrete Optimization - Mathematics (EDOM)


External institutions with authors

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


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.

BibTeX: 

Last updated on 2018-08-08 at 02:39