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.
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Produktdetaljer
ISBN
9781475767988
Publisert
2020
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter