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OverviewThis book is the result of 18 years of research into Steiner's problem and its relatives in theory and application. Starting with investigations of shortest networks for VLSI layout and, on the other hand, for certain facility location problems, the author has found many common properties for Steiner's problem in various spaces. The purpose of the book is to sum up and generalize many of these results for arbitrary finite-dimensional Banach spaces. It shows that we can create a homogeneous and general theory when we consider two dimensions of such spaces, and that we can find many facts which are helpful in attacking Steiner's problem in the higher-dimensional cases. The author examines the underlying mathematical properties of this network design problem and demonstrates how it can be attacked by various methods of geometry, graph theory, calculus, optimization and theoretical computer science. Audience: All mathematicians and users of applied graph theory. Full Product DetailsAuthor: Dietmar CieslikPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of hardcover 1st ed. 1998 Volume: 23 Dimensions: Width: 15.50cm , Height: 1.70cm , Length: 23.50cm Weight: 0.522kg ISBN: 9781441947901ISBN 10: 1441947906 Pages: 322 Publication Date: 07 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 Introduction.- 2 SMT and MST in Metric Spaces — A Survey.- 3 Fermat’s Problem in Banach-Minkowski Spaces.- 4 The Degrees of the Vertices in Shortest Trees.- 5 1-Steiner-Minimal-Trees.- 6 Methods to Construct Shortest Trees.- 7 The Steiner Ratio of Banach-Minkowski Spaces.- 8 Generalizations.- References.Reviews'In summary, this is a well written book on an interesting and challenging range of problems but from a mathematician's viewpoint. As such it can be strongly recommended.' Journal of the Operational Research Society, 49:12 (1998) 'The book has an encyclopedic character, contains lots of information and seems a must for those interested in the subject.' Nieuw Archief voor Wiskunde, 5/1:1 (2000) `In summary, this is a well written book on an interesting and challenging range of problems but from a mathematician's viewpoint. As such it can be strongly recommended.' Journal of the Operational Research Society, 49:12 (1998) `The book has an encyclopedic character, contains lots of information and seems a must for those interested in the subject.' Nieuw Archief voor Wiskunde, 5/1:1 (2000) 'In summary, this is a well written book on an interesting and challenging range of problems but from a mathematician's viewpoint. As such it can be strongly recommended.' Journal of the Operational Research Society, 49:12 (1998) 'The book has an encyclopedic character, contains lots of information and seems a must for those interested in the subject.' Nieuw Archief voor Wiskunde, 5/1:1 (2000) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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