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The Steiner Tree Problem Hans Jurgen Proemel

The Steiner Tree Problem By Hans Jurgen Proemel

The Steiner Tree Problem by Hans Jurgen Proemel

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Summary

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.

The Steiner Tree Problem Summary

The Steiner Tree Problem: A Tour through Graphs, Algorithms, and Complexity by Hans Jurgen Proemel

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.

The Steiner Tree Problem 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

About Hans Jurgen Proemel

Prof. Dr. Jurgen Proemel ist am Institut fur Informatik der Humboldt Universitat zu Berlin tatig, Prof. Dr. Angelika Steger lehrt am Institut fur Informatik der TU Munchen.

Table of Contents

1 Basics I: Graphs.- 1.1 Introduction to graph theory.- 1.2 Excursion: Random graphs.- 2 Basics II: Algorithms.- 2.1 Introduction to algorithms.- 2.2 Excursion: Fibonacci heaps and amortized time.- 3 Basics III: Complexity.- 3.1 Introduction to complexity theory.- 3.2 Excursion: More NP-complete problems.- 4 Special Terminal Sets.- 4.1 The shortest path problem.- 4.2 The minimum spanning tree problem.- 4.3 Excursion: Matroids and the greedy algorithm.- 5 Exact Algorithms.- 5.1 The enumeration algorithm.- 5.2 The Dreyfus-Wagner algorithm.- 5.3 Excursion: Dynamic programming.- 6 Approximation Algorithms.- 6.1 A simple algorithm with performance ratio 2.- 6.2 Improving the time complexity.- 6.3 Excursion: Machine scheduling.- 7 More on Approximation Algorithms.- 7.1 Minimum spanning trees in hypergraphs.- 7.2 Improving the performance ratio I.- 7.3 Excursion: The complexity of optimization problems.- 8 Randomness Helps.- 8.1 Probabilistic complexity classes.- 8.2 Improving the performance ratio II.- 8.3 An almost always optimal algorithm.- 8.4 Excursion: Primality and cryptography.- 9 Limits of Approximability.- 9.1 Reducing optimization problems.- 9.2 APX-completeness.- 9.3 Excursion: Probabilistically checkable proofs.- 10 Geometric Steiner Problems.- 10.1 A characterization of rectilinear Steiner minimum trees.- 10.2 The Steiner ratios.- 10.3 An almost linear time approximation scheme.- 10.4 Excursion: The Euclidean Steiner problem.- Symbol Index.

Additional information

NLS9783528067625
9783528067625
3528067624
The Steiner Tree Problem: A Tour through Graphs, Algorithms, and Complexity by Hans Jurgen Proemel
Hans Jurgen Proemel
Advanced Lectures in Mathematics
New
Paperback
Springer Fachmedien Wiesbaden
2002-02-25
241
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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