The Steiner Tree Problem : A Tour through Graphs, Algorithms, and Complexity

Promel, Hans Jurgen

ISBN 10: 3528067624 / ISBN 13: 9783528067625

Published by Vieweg+Teubner Verlag 2002-02, 2002

About this Item

Seller Inventory # 6666-IUK-9783528067625

Bibliographic Details

• Title: The Steiner Tree Problem : A Tour through Graphs, Algorithms, and Complexity
• Publisher: Vieweg+Teubner Verlag 2002-02
• Publication Date: 2002
• Language: English
• ISBN 10: 3528067624
• ISBN 13: 9783528067625
• Binding: PF
• Condition: New

About this title

Synopsis

"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.

About the Author

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.