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Packing steiner trees: polyhedral investigations (1992).
| Content Provider | CiteSeerX |
|---|---|
| Author | Grötschel, M. Martin, A. Weismantel, R. |
| Abstract | Let G = (V; E) be a graph and T ` V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V; E) with edge weights w e, edge capacities c e; e 2 E; and node sets T 1; : : : ; TN, find edge sets S 1; : : : ; SN such that each S k is a Steiner tree with respect to T k, at most c e of these edge sets use edge e for each e 2 E, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSIdesign, 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 appropriate 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 [GMW92]. |
| File Format | |
| Publisher Date | 1992-01-01 |
| Access Restriction | Open |
| Subject Keyword | Steiner Tree Polyhedral Investigation Edge Set Node Set Polyhedral Point Steiner Tree Polyhedron Facet-defining Inequality Following Problem Weighted Steiner Tree Branch Cut Algorithm Mild Assumption Main Emphasis Kind Involve Edge Weight Companion Paper Gmw92 Edge Capacity Appropriate Polyhedron So-called Joint Inequality |
| Content Type | Text |
| Resource Type | Article |
