Class Steiner trees and VLSI-design

Class Steiner Trees and VLSI-design

We consider a generalized version of the Steiner problem in graphs, motivated by the wire routing phase in physical VLSI design: given a connected, undirected distance graph with required classes of vertices and Steiner vertices, find a shortest connected subgraph containing at least one vertex of each required class. We show that this problem is NP-hard, even if there are no Steiner vertices a...

Rectilinear group Steiner trees and applications in VLSI design

Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of nding a shortest intercon-nection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the well-known rectilinear Steiner tree problem which has direct applications in VLSI design, i.e., it is the fundamental prob...

Shortest Paths and Steiner Trees in VLSI Routing

Die Theorie ist nicht die Wurzel, sondern die Blüte der Praxis. Acknowledgments I would like to express my gratitude to my supervisors, Professor Dr. Bernhard Korte and Professor Dr. Jens Vygen. I benefited a lot from their ideas, experience and guidance. This work would not have been possible without them, and I am happy to be part of their research team. Under their leading, the Research Inst...

Steiner Trees and Steiner Forests

The Steiner tree packing problem in VLSI design

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switch-box routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we deve...