Combinatorial optimization: networks and matroids
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Mineola, NY
Dover Publ.
2001
|
Ausgabe: | 1. publ., unabridged reprint ... [der Ausg.] 1976 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | X, 374 S. graph. Darst. |
ISBN: | 0486414531 |
Internformat
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100 | 1 | |a Lawler, Eugene L. |e Verfasser |4 aut | |
245 | 1 | 0 | |a Combinatorial optimization |b networks and matroids |c Eugene Lawler |
250 | |a 1. publ., unabridged reprint ... [der Ausg.] 1976 | ||
264 | 1 | |a Mineola, NY |b Dover Publ. |c 2001 | |
300 | |a X, 374 S. |b graph. Darst. | ||
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650 | 7 | |a Otimização combinatória |2 larpcal | |
650 | 4 | |a Algorithms | |
650 | 4 | |a Combinatorial optimization | |
650 | 4 | |a Computational complexity | |
650 | 4 | |a Matroids | |
650 | 4 | |a Network analysis (Planning) | |
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Datensatz im Suchindex
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adam_text |
Contents
Preface iii
Chapter 1
INTRODUCTION 1
1. What is Combinatorial Optimization? 1
2. Some Representative Optimization Problems 2
3. When is a Problem Solved? 4
4. The Criterion of Polynomial Boundedness 5
5. Some Apparently Nonpolynomial Bounded Problems 8
6. Methods of Solution 10
Comments and References 12
Chapter 2
MATHEMATICAL PRELIMINARIES 15
1. Mathematical Prerequisites 15
2. Sets and Relations 16
3. Graphs and Digraphs 20
4. Subgraphs, Cliques, Multigraphs 24
5. Connectivity in Graphs 26
6. Connectivity in Digraphs 28
7. Cocycles and Directed Cocycles 31
8. Planarity and Duality 32
9. Eulerian and Hamiltonian Graphs 36
10. Linear Programming Problems 39
11. The Simplex Method 43
12. Geometric Interpretation 48
13. Duality Theory 53
Comments and References 58
vii
Chapter 3
SHORTEST PATHS 59
1. Introduction 59
2. Some Problem Formulations 61
3. Bellmans Equations 65
4. Acyclic Networks 68
5. Networks with Positive Arcs: Dijkstra's Method 70
6. Solution by Successive Approximations: Bellman Ford Method
Method 74
7. Improvements in Efficiency: Yen's Modifications 76
8. Linear Programming Interpretation and Relaxation
Procedures 77
9. Shortest Paths between all Pairs of Nodes: Matrix
Multiplication 82
10. Floyd Warshall Method 86
11. Detection of Negative Cycles 90
12. Networks with Transit Times 92
13. The Minimal Cost to time Ratio Cycle Problem 94
14. M Shortest Paths: Dreyfus Method 98
15. M Shortest Paths without Repeated Nodes 100
Comments and References 104
Chapter 4
NETWORK FLOWS 109
1. Introduction 109
2. Maximal Flows 110
3. Maximal Flow Algorithm 114
4. Efficiency of the Maximal Flow Algorithm 116
5. Combinatorial Implications of Max Flow Min Cut Theorem 120
6. Linear Programming Interpretation of Max Flow Min Cut
Theorem 123
7. Minimum Cost Flows 129
8. Networks with Losses and Gains 134
9. Lower Bounds and Circulations 138
10. The Out of Kilter Method 142
11. Theoretical Improvement in Efficiency of Out of Kilter
Method 157
12. Integrality of Flows and the Unimodular Property 160
13. Application to Project Scheduling 165
14. Transhipment and Transportation Problems 169
viii
15. Multiterminal and Multicommodity Flows 173
Comments and References 177
Chapter 5
BIPARTITE MATCHING 182
1. Introduction 182
2. Problem Reductions and Equivalences 184
3. Counterparts of Network Flow Theorems 188
4. Mendelsohn Dulmage Theorem 191
5. Cardinality Matching Algorithm 193
6. A Special Case: Convex Graphs 196
7. Max Min Matching 197
8. The Hungarian Method for Weighted Matching 201
9. A Special Case: Gilmore Gomory Matching 207
10. A Novel Optimization Criterion: Gale Shapley Matching 211
Comments and References 214
Chapter 6
NONBIPARTITE MATCHING 217
1. Introduction 217
2. Problem Formulations 218
3. Bidirected Flows 223
4. Augmenting Paths 226
5. Trees and Blossoms 229
6. Cardinality Matching Algorithm 233
7. Duality Theory 239
8. Linear Programming Formulation of Weighted Matching
Problem 242
9. An O(n*) Weighted Matching Algorithm 247
10. An O(n3) Weighted Matching Algorithm 252
11. The Chinese Postman's Problem 259
Comments and References 261
Chapter 7
MATROIDS AND THE GREEDY ALGORITHM 264
1. Introduction 264
2. Three Apparently Unrelated Optimization Problems 265
3. Matroid Definitions 268
4. Matching, Transversal, and Partition Matroids 271
ix
5. Matroid Axiomatics 273
6. The Matroid Greedy Algorithm 275
7. Applications of the Greedy Algorithm 278
8. Matroid Duality 280
9. Variations of the Greedy Algorithm 283
10. Prim Spanning Tree Algorithm 285
11. An Application: Flow Network Synthesis 286
12. The Steiner Problem and Other Dilemmas 290
Comments and References 296
Chapter 8
MATROID INTERSECTIONS 300
1. Introduction 300
2. Problem Formulations 301
3. Augmenting Sequences and Border Graphs 306
4. Cardinality Intersection Algorithm 313
5. Duality Theory 315
6. Generalized Mendelsohn Dulmage Theorem, Matroid Sums
and Matroid Partitions 317
7. Matroid Partitioning Algorithm 320
8. The Shannon Switching Game 324
9. Weighted Augmenting Sequences 326
10. Primal Weighted Intersection Algorithm 332
11. Matroid Polyhedra 334
12. Explanation of Primal Dual Method 339
13. Primal Dual Weighted Intersection Algorithm 345
14. A Special Case: Directed Spanning Trees 348
Comments and References 352
Chapter 9
THE MATROID PARITY PROBLEM 356
1. Introduction 356
2. Problem Formulations 358
3. Augmenting Sequences 363
4. Generalizations 364
Comments and References 367
Author Index 368
Subject Index 371
x |
any_adam_object | 1 |
author | Lawler, Eugene L. |
author_facet | Lawler, Eugene L. |
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author_sort | Lawler, Eugene L. |
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dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.3 |
dewey-search | 519.3 |
dewey-sort | 3519.3 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
edition | 1. publ., unabridged reprint ... [der Ausg.] 1976 |
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id | DE-604.BV013886446 |
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institution | BVB |
isbn | 0486414531 |
language | English |
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spelling | Lawler, Eugene L. Verfasser aut Combinatorial optimization networks and matroids Eugene Lawler 1. publ., unabridged reprint ... [der Ausg.] 1976 Mineola, NY Dover Publ. 2001 X, 374 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Otimização combinatória larpcal Algorithms Combinatorial optimization Computational complexity Matroids Network analysis (Planning) Graphentheorie (DE-588)4113782-6 gnd rswk-swf Matroid (DE-588)4128705-8 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Netzplantechnik (DE-588)4075297-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Netzwerk (DE-588)4171529-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Matroid (DE-588)4128705-8 s Kombinatorische Optimierung (DE-588)4031826-6 s DE-604 Netzplantechnik (DE-588)4075297-5 s Netzwerk (DE-588)4171529-9 s Algorithmus (DE-588)4001183-5 s 1\p DE-604 Optimierung (DE-588)4043664-0 s 2\p DE-604 Graphentheorie (DE-588)4113782-6 s 3\p DE-604 Mathematik (DE-588)4037944-9 s 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009500145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Lawler, Eugene L. Combinatorial optimization networks and matroids Otimização combinatória larpcal Algorithms Combinatorial optimization Computational complexity Matroids Network analysis (Planning) Graphentheorie (DE-588)4113782-6 gnd Matroid (DE-588)4128705-8 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Mathematik (DE-588)4037944-9 gnd Netzplantechnik (DE-588)4075297-5 gnd Optimierung (DE-588)4043664-0 gnd Netzwerk (DE-588)4171529-9 gnd Algorithmus (DE-588)4001183-5 gnd |
subject_GND | (DE-588)4113782-6 (DE-588)4128705-8 (DE-588)4031826-6 (DE-588)4037944-9 (DE-588)4075297-5 (DE-588)4043664-0 (DE-588)4171529-9 (DE-588)4001183-5 |
title | Combinatorial optimization networks and matroids |
title_auth | Combinatorial optimization networks and matroids |
title_exact_search | Combinatorial optimization networks and matroids |
title_full | Combinatorial optimization networks and matroids Eugene Lawler |
title_fullStr | Combinatorial optimization networks and matroids Eugene Lawler |
title_full_unstemmed | Combinatorial optimization networks and matroids Eugene Lawler |
title_short | Combinatorial optimization |
title_sort | combinatorial optimization networks and matroids |
title_sub | networks and matroids |
topic | Otimização combinatória larpcal Algorithms Combinatorial optimization Computational complexity Matroids Network analysis (Planning) Graphentheorie (DE-588)4113782-6 gnd Matroid (DE-588)4128705-8 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Mathematik (DE-588)4037944-9 gnd Netzplantechnik (DE-588)4075297-5 gnd Optimierung (DE-588)4043664-0 gnd Netzwerk (DE-588)4171529-9 gnd Algorithmus (DE-588)4001183-5 gnd |
topic_facet | Otimização combinatória Algorithms Combinatorial optimization Computational complexity Matroids Network analysis (Planning) Graphentheorie Matroid Kombinatorische Optimierung Mathematik Netzplantechnik Optimierung Netzwerk Algorithmus |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009500145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT lawlereugenel combinatorialoptimizationnetworksandmatroids |