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The Steiner tree problem: a tour through graphs, algorithms, and complexity

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Bibliographic Details
Main Authors:	Prömel, Hans Jürgen 1953- (Author), Steger, Angelika 1962- (Author)
Format:	Book
Language:	English
Published:	Braunschweig [u.a.] Vieweg 2002
Edition:	1. ed.
Series:	Advanced lectures in mathematics
Subjects:	Algorithmes Algoritmen Bomen (wiskunde) Complexité de calcul (Informatique) Grafentheorie Graphes, Théorie des Steiner, Systèmes de Algorithms Computational complexity Graph theory Steiner systems Steiner-Problem Komplexitätstheorie Steiner-Baum Algorithmus
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009698726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	VII, 241 S. Ill., graph. Darst.
ISBN:	3528067624

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adam_text	HANS JURGEN PROMEL ANGELIKA STEGER THE STEINER TREE PROBLEM A TOUR THROUGH GRAPHS, ALGORITHMS, AND COMPLEXITY VIEWEG CONTENTS 1 BASICS I: GRAPHS 1 1.1 INTRODUCTION TO GRAPH THEORY 1 1.2 EXCURSION: RANDOM GRAPHS 9 2 BASICS II: ALGORITHMS 23 2.1 INTRODUCTION TO ALGORITHMS 23 2.2 - EXCURSION: FIBONACCI HEAPS AND AMORTIZED TIME 31 3 BASICS III: COMPLEXITY 41 3.1 INTRODUCTION TO COMPLEXITY THEORY 42 3.2 EXCURSION: MORE NP-COMPLETE PROBLEMS 51 4 SPECIAL TERMINAL SETS 63 4.1 THE SHORTEST PATH PROBLEM 63 4.2 THE MINIMUM SPANNING TREE PROBLEM 66 4.3 EXCURSION: MATROIDS AND THE GREEDY ALGORITHM 68 5 EXACT ALGORITHMS 75 5.1 THE ENUMERATION ALGORITHM 76 5.2 THE DREYFUS-WAGNER ALGORITHM 78 5.3 EXCURSION: DYNAMIC PROGRAMMING 81 6 APPROXIMATION ALGORITHMS 87 6.1 A SIMPLE ALGORITHM WITH PERFORMANCE RATIO 2 88 6.2 IMPROVING THE TIME COMPLEXITY 90 6.3 EXCURSION: MACHINE SCHEDULING 95 VIII 7 MORE ON APPROXIMATION ALGORITHMS 107 7.1 MINIMUM SPANNING TREES IN HYPERGRAPHS 108 7.2 IMPROVING THE PERFORMANCE RATIO I 116 7.3 EXCURSION: THE COMPLEXITY OF OPTIMIZATION PROBLEMS 121 8 RANDOMNESS HELPS 133 8.1 PROBABILISTIC COMPLEXITY CLASSES 133 8.2 IMPROVING THE PERFORMANCE RATIO II 139 8.3 AN ALMOST ALWAYS OPTIMAL ALGORITHM 148 8.4 EXCURSION: PRIMALITY AND CRYPTOGRAPHY 152 9 LIMITS OF APPROXIMABILITY 165 9.1 REDUCING OPTIMIZATION PROBLEMS 165 9.2 APX-COMPLETENESS 174 9.3 EXCURSION: PROBABILISTICALLY CHECKABLE PROOFS 179 10 GEOMETRIC STEINER PROBLEMS 191 10.1 A CHARACTERIZATION OF RECTILINEAR STEINER MINIMUM TREES . . . . 192 10.2 THE STEINER RATIOS 199 10.3 AN ALMOST LINEAR TIME APPROXIMATION SCHEME 204 10.4 EXCURSION: THE EUCLIDEAN STEINER PROBLEM 212 BIBLIOGRAPHY 223 INDEX 233 SYMBOL INDEX 241
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author	Prömel, Hans Jürgen 1953- Steger, Angelika 1962-
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series2	Advanced lectures in mathematics
spellingShingle	Prömel, Hans Jürgen 1953- Steger, Angelika 1962- The Steiner tree problem a tour through graphs, algorithms, and complexity Algorithmes Algoritmen gtt Bomen (wiskunde) gtt Complexité de calcul (Informatique) Grafentheorie gtt Graphes, Théorie des Steiner, Systèmes de Algorithms Computational complexity Graph theory Steiner systems Steiner-Problem (DE-588)4248342-6 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Steiner-Baum (DE-588)4228498-3 gnd Algorithmus (DE-588)4001183-5 gnd
subject_GND	(DE-588)4248342-6 (DE-588)4120591-1 (DE-588)4228498-3 (DE-588)4001183-5
title	The Steiner tree problem a tour through graphs, algorithms, and complexity
title_auth	The Steiner tree problem a tour through graphs, algorithms, and complexity
title_exact_search	The Steiner tree problem a tour through graphs, algorithms, and complexity
title_full	The Steiner tree problem a tour through graphs, algorithms, and complexity Hans Jürgen Prömel ; Angelika Steger
title_fullStr	The Steiner tree problem a tour through graphs, algorithms, and complexity Hans Jürgen Prömel ; Angelika Steger
title_full_unstemmed	The Steiner tree problem a tour through graphs, algorithms, and complexity Hans Jürgen Prömel ; Angelika Steger
title_short	The Steiner tree problem
title_sort	the steiner tree problem a tour through graphs algorithms and complexity
title_sub	a tour through graphs, algorithms, and complexity
topic	Algorithmes Algoritmen gtt Bomen (wiskunde) gtt Complexité de calcul (Informatique) Grafentheorie gtt Graphes, Théorie des Steiner, Systèmes de Algorithms Computational complexity Graph theory Steiner systems Steiner-Problem (DE-588)4248342-6 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Steiner-Baum (DE-588)4228498-3 gnd Algorithmus (DE-588)4001183-5 gnd
topic_facet	Algorithmes Algoritmen Bomen (wiskunde) Complexité de calcul (Informatique) Grafentheorie Graphes, Théorie des Steiner, Systèmes de Algorithms Computational complexity Graph theory Steiner systems Steiner-Problem Komplexitätstheorie Steiner-Baum Algorithmus
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009698726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT promelhansjurgen thesteinertreeproblematourthroughgraphsalgorithmsandcomplexity AT stegerangelika thesteinertreeproblematourthroughgraphsalgorithmsandcomplexity

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