The Steiner Tree Problem: A Tour through Graphs, Algorithms, and Complexity (Advanced Lectures in Mathematics) - Softcover

Promel, Hans Jurgen

Softcover

ISBN 10: 3528067624 ISBN 13: 9783528067625

Publisher: Vieweg+Teubner Verlag, 2002

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 this title

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.

From the Back Cover

In recent years, algorithmic graph theory has become increasingly important as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graphs theory, algorithms and complexity. No specific previous knowledge is assumed.
The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner problem, was initially of importance only within the context of land surveying. In the last decade, however, applications as diverse as VLSI-layout and the study of phylogenetic trees led to a rapid rise of interest in this problem. The resulting progress has uncovered fascinating connections between and within graph theory, the study of algorithms, and complexity theory. This single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms, computational complexity, approximation algorithms, the use of randomness, limits of approximability.
A special feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner problem by placing them in a broader context.

Edition details

• Publisher: Vieweg+Teubner Verlag
• Publication date: 2002
• Language: English
• ISBN 10: 3528067624
• ISBN 13: 9783528067625
• Binding: Paperback
• Number of pages: 249