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Steiner Minimal Trees (Hardcover, 1998 ed.)
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Steiner Minimal Trees (Hardcover, 1998 ed.)
Series: Nonconvex Optimization and Its Applications, 23
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The problem of "Shortest Connectivity," which is discussed here,
has a long and convoluted history. Many scientists from many fields
as well as laymen have stepped on its stage. Usually, the problem
is known as Steiner's Problem and it can be described more
precisely in the following way: Given a finite set of points in a
metric space, search for a network that connects these points with
the shortest possible length. This shortest network must be a tree
and is called a Steiner Minimal Tree (SMT). It may contain vertices
different from the points which are to be connected. Such points
are called Steiner points. Steiner's Problem seems disarmingly
simple, but it is rich with possibilities and difficulties, even in
the simplest case, the Euclidean plane. This is one of the reasons
that an enormous volume of literature has been published, starting
in 1 the seventeenth century and continuing until today. The
difficulty is that we look for the shortest network overall.
Minimum span ning networks have been well-studied and solved
eompletely in the case where only the given points must be
connected. The novelty of Steiner's Problem is that new points, the
Steiner points, may be introduced so that an intercon necting
network of all these points will be shorter. This also shows that
it is impossible to solve the problem with combinatorial and
geometric methods alone."
General
Imprint: |
Springer
|
Country of origin: |
Netherlands |
Series: |
Nonconvex Optimization and Its Applications, 23 |
Release date: |
2001 |
First published: |
March 1998 |
Authors: |
Dietmar Cieslik
|
Dimensions: |
234 x 156 x 20mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
322 |
Edition: |
1998 ed. |
ISBN-13: |
978-0-7923-4983-9 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Combinatorics & graph theory
|
LSN: |
0-7923-4983-0 |
Barcode: |
9780792349839 |
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