The Steiner Ratio
DOWNLOAD
Download The Steiner Ratio PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Steiner Ratio book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Steiner Ratio
DOWNLOAD
Author : Dietmar Cieslik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Steiner Ratio written by Dietmar Cieslik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.
Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms.
A Proof Of Gilbert Pollak S Conjecture On The Steiner Ratio
DOWNLOAD
Author : DIMACS (GROUP)
language : en
Publisher:
Release Date : 1990
A Proof Of Gilbert Pollak S Conjecture On The Steiner Ratio written by DIMACS (GROUP) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Steiner systems categories.
Abstract: "Let P be a set of n points on the euclidean plane. Let L[subscript s](P) and L[subscript m](P) denote the lengths of the Steiner minimum tree and the minimum spanning tree on P, respectively. In 1968, Gilbert and Pollak conjectured that for any P, [formula]. We provide a proof for their conjecture in this paper."
The Steiner Ratio For The Obstacle Avoiding Steiner Tree Problem
DOWNLOAD
Author : Mina Razaghpour
language : en
Publisher:
Release Date : 2008
The Steiner Ratio For The Obstacle Avoiding Steiner Tree Problem written by Mina Razaghpour and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
This thesis examines the (geometric) Steiner tree problem: Given a set of points P in the plane, find a shortest tree interconnecting all points in P, with the possibility of adding points outside P, called the Steiner points, as additional vertices of the tree. The Steiner tree problem has been studied in different metric spaces. In this thesis, we study the problem in Euclidean and rectilinear metrics. One of the most natural heuristics for the Steiner tree problem is to use a minimum spanning tree, which can be found in O(nlogn) time . The performance ratio of this heuristic is given by the Steiner ratio, which is defined as the minimum possible ratio between the lengths of a minimum Steiner tree and a minimum spanning tree. We survey the background literature on the Steiner ratio and study the generalization of the Steiner ratio to the case of obstacles. We introduce the concept of an anchored Steiner tree: an obstacle-avoiding Steiner tree in which the Steiner points are only allowed at obstacle corners. We define the obstacle-avoiding Steiner ratio as the ratio of the length of an obstacle-avoiding minimum Steiner tree to that of an anchored obstacle-avoiding minimum Steiner tree. We prove that, for the rectilinear metric, the obstacle-avoiding Steiner ratio is equal to the traditional (obstacle-free) Steiner ratio. We conjecture that this is also the case for the Euclidean metric and we prove this conjecture for three points and any number of obstacles.
Critical Points For The Steiner Ratio Conjecture
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1989
Critical Points For The Steiner Ratio Conjecture written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
The Steiner Ratio Conjecture For Cocircular Points
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1989
The Steiner Ratio Conjecture For Cocircular Points written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
The Steiner Ratio Conjecture For Six Points
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1989
The Steiner Ratio Conjecture For Six Points written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
A Simple Proof Of The Steiner Ratio Conjecture For Five Points
DOWNLOAD
Author : J. Friedel
language : en
Publisher:
Release Date : 1988
A Simple Proof Of The Steiner Ratio Conjecture For Five Points written by J. Friedel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
The Steiner Tree Problem
DOWNLOAD
Author : F.K. Hwang
language : en
Publisher: Elsevier
Release Date : 1992-10-20
The Steiner Tree Problem written by F.K. Hwang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-20 with Computers categories.
The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging. The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.
The Steiner Ratio For Five Points
DOWNLOAD
Author : Raymond Sydney Booth
language : en
Publisher:
Release Date : 1991
The Steiner Ratio For Five Points written by Raymond Sydney Booth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Steiner systems categories.
Improved Upper Bounds For The Steiner Ratio
DOWNLOAD
Author : Victoria Garritan
language : en
Publisher:
Release Date : 2011
Improved Upper Bounds For The Steiner Ratio written by Victoria Garritan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometry, Projective categories.
