Network flows: theory, algorithms, and applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Prentice Hall
1993
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XV, 846 S. graph. Darst. |
| ISBN: | 013617549X |
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| 264 | 1 | |a Upper Saddle River, NJ |b Prentice Hall |c 1993 | |
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Datensatz im Suchindex
| _version_ | 1804122534641139712 |
|---|---|
| adam_text | CONTENTS
PREFACE, xi
1 INTRODUCTION, 1
1.1 Introduction, 1
1.2 Network Flow Problems, 4
1.3 Applications, 9
1.4 Summary, 18
Reference Notes, 19
Exercises, 20
2 PATHS, TREES, AND CYCLES, 23
2.1 Introduction, 23
2.2 Notation and Definitions, 24
2.3 Network Representations, 31
2.4 Network Transformations, 38
2.5 Summary, 46
Reference Notes, 47
Exercises, 47
3 ALGORITHM DESIGN AND ANALYSIS, 53
3.1 Introduction, 53
3.2 Complexity Analysis, 56
3.3 Developing Polynomial Time Algorithms, 66
3.4 Search Algorithms, 73
3.5 Flow Decomposition Algorithms, 79
3.6 Summary, 84
Reference Notes, 85
Exercises, 86
4 SHORTEST PATHS: LABEL SETTING ALGORITHMS, 93
4.1 Introduction, 93
4.2 Applications, 97
4.3 Tree of Shortest Paths, 106
4.4 Shortest Path Problems in Acyclic Networks, 107
4.5 Dijkstra s Algorithm, 108
4.6 Dial s Implementation, 113
A.I Heap Implementations, 115
4.8 Radix Heap Implementation, 116
4.9 Summary, 121
Reference Notes, 122
Exercises, 124
5 SHORTEST PA THS: LABEL CORRECTING ALGORITHMS, 133
5.1 Introduction, 133
5.2 Optimality Conditions, 135
5.3 Generic Label Correcting Algorithms, 136
5.4 Special Implementations of the Modified Label Correcting Algorithm, 141
5.5 Detecting Negative Cycles, 143
5.6 All Pairs Shortest Path Problem, 144
5.7 Minimum Cost to Time Ratio Cycle Problem, 150
5.8 Summary, 154
Reference Notes, 156
Exercises, 157
6 MAXIMUM FLOWS: BASIC IDEAS, 166
6.1 Introduction, 166
6.2 Applications, 169
6.3 Flows and Cuts, 177
6.4 Generic Augmenting Path Algorithm, 180
6.5 Labeling Algorithm and the Max Flow Min Cut Theorem, 184
6.6 Combinatorial Implications of the Max Flow Min Cut Theorem, 188
6.7 Flows with Lower Bounds, 191
6.8 Summary, 196
Reference Notes, 197
Exercises, 198
7 MAXIMUM FLOWS: POLYNOMIAL ALGORITHMS, 207
7.1 Introduction, 207
7.2 Distance Labels, 209
7.3 Capacity Scaling Algorithm, 210
1A Shortest Augmenting Path Algorithm, 213
7.5 Distance Labels and Layered Networks, 221
7.6 Generic Preflow Push Algorithm, 223
7.7 FIFO Preflow Push Algorithm, 231
7.8 Highest Label Preflow Push Algorithm, 233
7.9 Excess Scaling Algorithm, 237
7.10 Summary, 241
Reference Notes, 241
Exercises, 243
8 MAXIMUM FLOWS: ADDITIONAL TOPICS, 250
8.1 Introduction, 250
8.2 Flows in Unit Capacity Networks, 252
8.3 Flows in Bipartite Networks, 255
8.4 Flows in Planar Undirected Networks, 260
8.5 Dynamic Tree Implementations, 265
vi Contents
8.6 Network Connectivity, 273
8.7 All Pairs Minimum Value Cut Problem, 277
8.8 Summary, 285
Reference Notes, 287
Exercises, 288
9 MINIMUM COST FLOWS: BASIC ALGORITHMS, 294
9.1 Introduction, 294
9.2 Applications, 298
9.3 Optimality Conditions, 306
9.4 Minimum Cost Flow Duality, 310
9.5 Relating Optimal Flows to Optimal Node Potentials, 315
9.6 Cycle Canceling Algorithm and the Integrality Property, 317
9.7 Successive Shortest Path Algorithm, 320
9.8 Primal Dual Algorithm, 324
9.9 Out of Kilter Algorithm, 326
9.10 Relaxation Algorithm, 332
9.11 Sensitivity Analysis, 337
9.12 Summary, 339
Reference Notes, 341
Exercises, 344
10 MINIMUM COST FLOWS: POLYNOMIAL ALGORITHMS, 357
10.1 Introduction, 357
10.2 Capacity Scaling Algorithm, 360
10.3 Cost Scaling Algorithm, 362
10.4 Double Scaling Algorithm, 373
10.5 Minimum Mean Cycle Canceling Algorithm, 376
10.6 Repeated Capacity Scaling Algorithm, 382
10.7 Enhanced Capacity Scaling Algorithm, 387
10.8 Summary, 395
Reference Notes, 396
Exercises, 397
11 MINIMUM COST FLOWS: NETWORK SIMPLEX ALGORITHMS, 402
11.1 Introduction, 402
11.2 Cycle Free and Spanning Tree Solutions, 405
11.3 Maintaining a Spanning Tree Structure, 409
11.4 Computing Node Potentials and Flows, 411
11.5 Network Simplex Algorithm, 415
11.6 Strongly Feasible Spanning Trees, 421
11.7 Network Simplex Algorithm for the Shortest Path Problem, 425
11.8 Network Simplex Algorithm for the Maximum Flow Problem, 430
11.9 Related Network Simplex Algorithms, 433
11.10 Sensitivity Analysis, 439
11.11 Relationship to Simplex Method, 441
11.12 Unimodularity Property, 447
11.13 Summary, 450
Reference Notes, 451
Exercises, 453
Contents vii
12 ASSIGNMENTS AND MATCHINGS, 461
12.1 Introduction, 461
12.2 Applications, 463
12.3 Bipartite Cardinality Matching Problem, 469
12.4 Bipartite Weighted Matching Problem, 470
12.5 Stable Marriage Problem, 473
12.6 Nonbipartite Cardinality Matching Problem, 475
12.7 Matchings and Paths, 494
12.8 Summary, 498
Reference Notes, 499
Exercises, 501
13 MINIMUM SPANNING TREES, 510
13.1 Introduction, 510
13.2 Applications, 512
13.3 Optimality Conditions, 516
13.4 Kruskal s Algorithm, 520
13.5 Prim s Algorithm, 523
13.6 Sollin s Algorithm, 526
13.7 Minimum Spanning Trees and Matroids, 528
13.8 Minimum Spanning Trees and Linear Programming, 530
13.9 Summary, 533
Reference Notes, 535
Exercises, 536
14 CONVEX COST FLOWS, 543
14.1 Introduction, 543
14.2 Applications, 546
14.3 Transformation to a Minimum Cost Flow Problem, 551
14.4 Pseudopolynomial Time Algorithms, 554
14.5 Polynomial Time Algorithm, 556
14.6 Summary, 560
Reference Notes, 567
Exercises, 562
15 GENERALIZED FLOWS, 566
15.1 Introduction, 566
15.2 Applications, 568
15.3 Augmented Forest Structures, 572
15.4 Determining Potentials and Flows for an Augmented Forest Structure, 577
15.5 Good Augmented Forests and Linear Programming Bases, 582
15.6 Generalized Network Simplex Algorithm, 583
15.7 Summary, 591
Reference Notes, 591
Exercises, 593
viii Contents
16 LAQRANGIAN RELAXATION AND NETWORK OPTIMIZATION, 598
16.1 Introduction, 598
16.2 Problem Relaxations and Branch and Bound, 602
16.3 Lagrangian Relaxation Technique, 605
16.4 Lagrangian Relaxation and Linear Programming, 615
16.5 Applications of Lagrangian Relaxation, 620
16.6 Summary, 635
Reference Notes, 637
Exercises, 638
17 MULTICOMMODITY FLOWS, 849
17.1 Introduction, 649
17.2 Applications, 653
17.3 Optimality Conditions, 657
17.4 Lagrangian Relaxation, 660
17.5 Column Generation Approach, 665
17.6 Dantzig Wolfe Decomposition, 677
17.7 Resource Directive Decomposition, 674
17.8 Basis Partitioning, 678
17.9 Summary, 682
Reference Notes, 684
Exercises, 686
18 COMPUTATIONAL TESTING OF ALGORITHMS, 690
18.1 Introduction, 695
18.2 Representative Operation Counts, 698
18.3 Application to Network Simplex Algorithm, 702
18.4 Summary, 713
Reference Notes, 713
Exercises, 715
19 ADDITIONAL APPLICATIONS, 717
19.1 Introduction, 717
19.2 Maximum Weight Closure of a Graph, 719
19.3 Data Scaling, 725
19.4 Science Applications, 728
19.5 Project Management, 732
19.6 Dynamic Flows, 737
19.7 Arc Routing Problems, 740
19.8 Facility Layout and Location, 744
19.9 Production and Inventory Planning, 748
19.10 Summary, 755
Reference Notes, 759
Exercises, 760
Contents ix
APPENDIX A DATA STRUCTURES, 765
A.I Introduction, 765
A.2 Elementary Data Structures, 766
A.3 rf Heaps, 773
A.4 Fibonacci Heaps, 779
Reference Notes, 787
APPENDIX B X9 COMPLETENESS, 788
B.I Introduction, 788
B.2 Problem Reductions and Transformations, 790
B.3 Problem Classes 9, J r9 , .^ Complete, and .VSP Hard, 792
B.4 Proving XSP Completeness Results, 796
B.5 Concluding Remarks, 800
Reference Notes, 801
APPENDIX C LINEAR PROGRAMMING, 802
C.I Introduction, 802
C.2 Graphical Solution Procedure, 804
C.3 Basic Feasible Solutions, 805
C.4 Simplex Method, 810
C.5 Bounded Variable Simplex Method, 814
C.6 Linear Programming Duality, 816
Reference Notes, 820
REFERENCES, 821
INDEX, 840
x Contents
|
| any_adam_object | 1 |
| author | Ahuja, Ravindra K. 1956- Magnanti, Thomas L. 1945- Orlin, James B. |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content Matériel didactique |
| genre_facet | Lehrbuch Matériel didactique |
| id | DE-604.BV008151217 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:15:24Z |
| institution | BVB |
| isbn | 013617549X |
| language | English |
| lccn | 92026702 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005378772 |
| oclc_num | 300741652 |
| open_access_boolean | |
| owner | DE-20 DE-384 DE-824 DE-739 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-N2 DE-703 DE-355 DE-BY-UBR DE-473 DE-BY-UBG DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-384 DE-824 DE-739 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-N2 DE-703 DE-355 DE-BY-UBR DE-473 DE-BY-UBG DE-634 DE-83 DE-11 DE-188 |
| physical | XV, 846 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Prentice Hall |
| record_format | marc |
| spelling | Ahuja, Ravindra K. 1956- Verfasser (DE-588)121654966 aut Network flows theory, algorithms, and applications Ravindra K. Ahuja ; Thomas L. Magnanti ; James B. Orlin Upper Saddle River, NJ Prentice Hall 1993 XV, 846 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse de réseau (Planification) Analyse de réseau (planification) ram Optimisation mathématique Optimisation mathématique ram algorithme polynomial inriac algorithme simplexe inriac complétude inriac coût minimum inriac flux inriac optimisation inriac plus court chemin inriac Network analysis (Planning) Mathematical optimization Netzwerkfluss (DE-588)4126130-6 gnd rswk-swf Netzwerkanalyse (DE-588)4075298-7 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Netzplantechnik (DE-588)4075297-5 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Matériel didactique Netzwerkanalyse (DE-588)4075298-7 s DE-604 Netzplantechnik (DE-588)4075297-5 s Netzwerkfluss (DE-588)4126130-6 s Optimierung (DE-588)4043664-0 s 2\p DE-604 Magnanti, Thomas L. 1945- Verfasser (DE-588)136531695 aut Orlin, James B. Verfasser (DE-588)170216128 aut application/pdf http://www.dandelon.com/intelligentSEARCH.nsf/metadetails?OpenFrameSet&ID=3513B27E539A5912C125793800743DB4&q=Network flows Magnanti, Thomas L.&media=B&searchterms=network,Netzwerk,netzwerk,Network,Netzwerk,flows,Magnanti,,Thomas,L. Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005378772&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 |
| spellingShingle | Ahuja, Ravindra K. 1956- Magnanti, Thomas L. 1945- Orlin, James B. Network flows theory, algorithms, and applications Analyse de réseau (Planification) Analyse de réseau (planification) ram Optimisation mathématique Optimisation mathématique ram algorithme polynomial inriac algorithme simplexe inriac complétude inriac coût minimum inriac flux inriac optimisation inriac plus court chemin inriac Network analysis (Planning) Mathematical optimization Netzwerkfluss (DE-588)4126130-6 gnd Netzwerkanalyse (DE-588)4075298-7 gnd Optimierung (DE-588)4043664-0 gnd Netzplantechnik (DE-588)4075297-5 gnd |
| subject_GND | (DE-588)4126130-6 (DE-588)4075298-7 (DE-588)4043664-0 (DE-588)4075297-5 (DE-588)4123623-3 |
| title | Network flows theory, algorithms, and applications |
| title_auth | Network flows theory, algorithms, and applications |
| title_exact_search | Network flows theory, algorithms, and applications |
| title_full | Network flows theory, algorithms, and applications Ravindra K. Ahuja ; Thomas L. Magnanti ; James B. Orlin |
| title_fullStr | Network flows theory, algorithms, and applications Ravindra K. Ahuja ; Thomas L. Magnanti ; James B. Orlin |
| title_full_unstemmed | Network flows theory, algorithms, and applications Ravindra K. Ahuja ; Thomas L. Magnanti ; James B. Orlin |
| title_short | Network flows |
| title_sort | network flows theory algorithms and applications |
| title_sub | theory, algorithms, and applications |
| topic | Analyse de réseau (Planification) Analyse de réseau (planification) ram Optimisation mathématique Optimisation mathématique ram algorithme polynomial inriac algorithme simplexe inriac complétude inriac coût minimum inriac flux inriac optimisation inriac plus court chemin inriac Network analysis (Planning) Mathematical optimization Netzwerkfluss (DE-588)4126130-6 gnd Netzwerkanalyse (DE-588)4075298-7 gnd Optimierung (DE-588)4043664-0 gnd Netzplantechnik (DE-588)4075297-5 gnd |
| topic_facet | Analyse de réseau (Planification) Analyse de réseau (planification) Optimisation mathématique algorithme polynomial algorithme simplexe complétude coût minimum flux optimisation plus court chemin Network analysis (Planning) Mathematical optimization Netzwerkfluss Netzwerkanalyse Optimierung Netzplantechnik Lehrbuch Matériel didactique |
| url | http://www.dandelon.com/intelligentSEARCH.nsf/metadetails?OpenFrameSet&ID=3513B27E539A5912C125793800743DB4&q=Network flows Magnanti, Thomas L.&media=B&searchterms=network,Netzwerk,netzwerk,Network,Netzwerk,flows,Magnanti,,Thomas,L. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005378772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ahujaravindrak networkflowstheoryalgorithmsandapplications AT magnantithomasl networkflowstheoryalgorithmsandapplications AT orlinjamesb networkflowstheoryalgorithmsandapplications |
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