The Steiner Tree Problem
A Tour through Graphs, Algorithms and Complexity
(Sprache: Englisch)
In recent years, algorithmic graph theory has become increasingly important since it serves as a link between discrete mathematics and theoretical computer science. This textbook presents an introduction to the interrelated fields of graph theory,...
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Produktinformationen zu „The Steiner Tree Problem “
In recent years, algorithmic graph theory has become increasingly important since it serves as a link between discrete mathematics and theoretical computer science. This textbook presents an introduction to the interrelated fields of graph theory, algorithms and complexity.
The main topics of this book are:
Exact Algorithms
Computational Complexity
Approximation Algorithms
Limits of Approximability
Randomness Helps
The Manhattan Steiner Problem
Heuristics
Packing of Steiner Trees
Applications
The main topics of this book are:
Exact Algorithms
Computational Complexity
Approximation Algorithms
Limits of Approximability
Randomness Helps
The Manhattan Steiner Problem
Heuristics
Packing of Steiner Trees
Applications
Klappentext zu „The Steiner Tree Problem “
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.
Inhaltsverzeichnis zu „The Steiner Tree Problem “
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.
Autoren-Porträt von Hans Jürgen Prömel, Angelika Steger
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.
Bibliographische Angaben
- Autoren: Hans Jürgen Prömel , Angelika Steger
- 2002, Softcover reprint of the original 1st ed. 2002, 241 Seiten, mit Abbildungen, Masse: 17 x 24 cm, Kartoniert (TB), Englisch
- Verlag: Vieweg+Teubner
- ISBN-10: 3528067624
- ISBN-13: 9783528067625
- Erscheinungsdatum: 25.02.2002
Sprache:
Englisch
Rezension zu „The Steiner Tree Problem “
"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
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