LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	004.0151
Title	The Steiner Ratio ([EBook] /) / by Dietmar Cieslik.
Author	Cieslik, Dietmar
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : : Springer US : : Imprint: Springer, , 2001.
Physical Details	XII, 244 p. : online resource.
Series	Combinatorial Optimization 1388-3011 ; ; 10
ISBN	9781475767988
Summary Note	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.:
Contents note	1 The Historical Genesis -- 2 Networks, Spaces and Algorithms -- 3 Shortest Trees in Metric Spaces — A Survey -- 4 The Steiner Ratio of Metric Spaces -- 5 The Steiner Ratio of Banach-Minkowski Spaces -- 6 Euclidean Spaces -- 7 The Steiner Ratio of Neighboured Spaces -- 8 Banach-Minkowski Planes -- 9 The Steiner Ratio and the Embedding of Spaces -- 10 The Steiner Ratio and Discrete Geometry -- 11 The Dependence of the Steiner Ratio on the Dimension -- 12 Related Questions -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-6798-8
Links to Related Works	Subject References: Algorithms . Computer Science . Convex and Discrete Geometry . Convex geometry . Discrete geometry . Discrete Mathematics in Computer Science . Mathematical optimization . Optimization . Authors: Cieslik, Dietmar . Corporate Authors: SpringerLink (Online service) . Series: Combinatorial Optimization . Classification: 004.0151 .

Catalogue Display

The Steiner Ratio

Reviews