Complexity and Approximation of the Rectilinear Steiner Tree Problem

Complexity and Approximation of the Rectilinear Steiner Tree Problem

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Given a finite set K of terminals in the plane. A rectilinear Steiner minimum tree for K (RST) is a tree which interconnects among these terminals using only horizontal and vertical lines of shortest possible length containing Steiner point. We show the complexity of RST i.e. belongs to NP-comp...

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Bibliographic Details
Main Author: Mussafi, Noor Saif Muhammad
Other Authors: Technische Universität Chemnitz
Format: Dissertation
Language:English
Published: 2009
Subjects:
info:eu-repo/classification/ddc/500
ddc:500
Angewandte Mathematik
Optimierungsproblem
Approximation Algorithm
Arora's Approximation Scheme
Graph Theory
The Steiner tree problem
The rectilinear Steiner tree problem
Online Access:http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901213
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Summary:Given a finite set K of terminals in the plane. A rectilinear Steiner minimum tree for K (RST) is a tree which interconnects among these terminals using only horizontal and vertical lines of shortest possible length containing Steiner point. We show the complexity of RST i.e. belongs to NP-complete. Moreover we present an approximative method of determining the solution of RST problem proposed by Sanjeev Arora in 1996, Arora's Approximation Scheme. This algorithm has time complexity polynomial in the number of terminals for a fixed performance ratio 1 + Epsilon.

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