# Vertex-Disjoint Packing of Two Steiner Trees: polyhedra and branch-and-cut

@article{Uchoa1999VertexDisjointPO, title={Vertex-Disjoint Packing of Two Steiner Trees: polyhedra and branch-and-cut}, author={Eduardo Uchoa and Marcus Poggi de Arag{\~a}o}, journal={Mathematical Programming}, year={1999}, volume={90}, pages={537-557} }

Abstract.Consider the problem of routing the electrical connections among two large terminal sets in circuit layout. A realistic model for this problem is given by the vertex-disjoint packing of two Steiner trees (2VPST), which is known to be NP-complete. This work presents an investigation on the 2VPST polyhedra. The main idea is to start from facet-defining inequalities for a vertex-weighted Steiner tree polyhedra. Some of these inequalities are proven to also define facets for the packing…

## 5 Citations

Rectilinear group Steiner trees and applications in VLSI design

- Computer Science, MathematicsMath. Program.
- 2003

This work presents a first (tailored) exact algorithm for solving the rectilinear group Steiner tree problem (and related variants of the problem) and experimental results for real-world VLSI instances with up to 100 groups are presented.

An approximate max-Steiner-tree-packing min-Steiner-cut theorem

- Mathematics, Computer Science45th Annual IEEE Symposium on Foundations of Computer Science
- 2004

It is proved that if the minimum S-cut in G has 26k edges, then G has at least k edge-disjoint S-trees; this answers Kriesell's conjecture affirmatively up to a constant multiple.

An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem*

- Mathematics, Computer ScienceComb.
- 2007

The main theorem is an approximate min-max relation between the maximum number of edge-disjoint trees that each connects S (S-trees) and the minimum size of an edge-cut that disconnects some pair of vertices in S (s-cut).

On approximate min-max theorems for graph connectivity problems

- Mathematics
- 2006

Given an undirected graph G and a subset of vertices S ⊆ V(G), we call the vertices in S the terminal vertices and the vertices in V (G) - S the Steiner vertices. In this thesis, we study two…

Preprocessing Steiner problems from VLSI layout

- Computer ScienceNetworks
- 2002

A new preprocessing procedure is proposed, extending earlier ideas from the literature and improving their application, so as to make them effective for VLSI problems, and significant reductions within reasonable computational times are reported.

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