Overview
- Authors:
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Hans Jürgen Prömel
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Institut für Informatik, Humboldt Universität zu Berlin, Berlin, Germany
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Angelika Steger
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Institut für Informatik, Technische Universität München, München, Germany
- Discrete mathematics in relation to computer science
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Table of contents (10 chapters)
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Front Matter
Pages I-VIII
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- Hans Jürgen Prömel, Angelika Steger
Pages 1-22
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- Hans Jürgen Prömel, Angelika Steger
Pages 23-40
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- Hans Jürgen Prömel, Angelika Steger
Pages 41-62
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- Hans Jürgen Prömel, Angelika Steger
Pages 63-74
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- Hans Jürgen Prömel, Angelika Steger
Pages 75-86
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- Hans Jürgen Prömel, Angelika Steger
Pages 87-106
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- Hans Jürgen Prömel, Angelika Steger
Pages 107-132
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- Hans Jürgen Prömel, Angelika Steger
Pages 133-164
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- Hans Jürgen Prömel, Angelika Steger
Pages 165-190
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- Hans Jürgen Prömel, Angelika Steger
Pages 191-222
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Back Matter
Pages 223-243
About this book
"A very simple but instructive problem was treated by Jacob Steiner, the famous representative of geometry at the University of Berlin in the early nineteenth century. Three villages A,B ,C are to be joined by a system of roads of minimum length. " Due to this remark of Courant and Robbins (1941), a problem received its name that actually reaches two hundred years further back and should more appropriately be attributed to the French mathematician Pierre Fermat. At the end of his famous treatise "Minima and Maxima" he raised the question to find for three given points in the plane a fourth one in such a way that the sum of its distances to the given points is minimized - that is, to solve the problem mentioned above in its mathematical abstraction. It is known that Evangelista Torricelli had found a geometrical solution for this problem already before 1640. During the last centuries this problem was rediscovered and generalized by many mathematicians, including Jacob Steiner. Nowadays the term "Steiner prob lem" refers to a problem where a set of given points PI, . . . ,Pn have to be connected in such a way that (i) any two of the given points are joined and (ii) the total length (measured with respect to some predefined cost function) is minimized.
Reviews
"The book is a very good introduction to discrete mathematics in relation to computer science, and a useful reference for those who are interested in network optimization problems." Zentralblatt MATH, Nr. 17/02
"This book is an excellent introduction to the Steiner tree problems, which starts with network Steiner trees an ends with geometric Steiner trees." Mathematical Reviews, Nr. 11/02
Authors and Affiliations
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Institut für Informatik, Humboldt Universität zu Berlin, Berlin, Germany
Hans Jürgen Prömel
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Institut für Informatik, Technische Universität München, München, Germany
Angelika Steger
About the authors
Prof. Dr. Jürgen Prömel ist am Institut für Informatik der Humboldt Universität zu Berlin tätig, Prof. Dr. Angelika Steger lehrt am Institut für Informatik der TU München.
