Combinatorial optimization: theory and algorithms
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2012
|
| Edition: | 5. ed. |
| Series: | Algorithms and combinatorics
21 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIX, 659 S. graph. Darst. 25 cm |
| ISBN: | 9783642244872 3642244874 9783642244889 |
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Record in the Search Index
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| adam_text |
IMAGE 1
TABLE OF CONTENTS
INTRODUCTION 1
1.1 ENUMERATION 2
1.2 RUNNING TIME OF ALGORITHMS 5
1.3 LINEAR OPTIMIZATION PROBLEMS 8
1.4 SORTING 9
EXERCISES 11
REFERENCES 12
GRAPHS 13
2.1 BASIC DEFINITIONS 13
2.2 TREES, CIRCUITS, AND CUTS 17
2.3 CONNECTIVITY 24
2.4 EULERIAN AND BIPARTITE GRAPHS 31
2.5 PLANARITY 34
2.6 PLANAR DUALITY 41
EXERCISES 43
REFERENCES 47
LINEAR PROGRAMMING 51
3.1 POLYHEDRA 52
3.2 THE SIMPLEX ALGORITHM 56
3.3 IMPLEMENTATION OF THE SIMPLEX ALGORITHM 60
3.4 DUALITY 63
3.5 CONVEX HULLS AND POLYTOPES 67
EXERCISES 68
REFERENCES 70
LINEAR PROGRAMMING ALGORITHMS 73
4.1 SIZE OF VERTICES AND FACES 73
4.2 CONTINUED FRACTIONS 76
4.3 GAUSSIAN ELIMINATION 79
4.4 THE ELLIPSOID METHOD 82
4.5 KHACHIYAN'S THEOREM 88
4.6 SEPARATION AND OPTIMIZATION 90
EXERCISES 97
REFERENCES 99
XV
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1016843828
DIGITALISIERT DURCH
IMAGE 2
XVI TABLE OF CONTENTS
5 INTEGER PROGRAMMING 101
5.1 THE INTEGER HULL OF A POLYHEDRON 103
5.2 UNIMODULAR TRANSFORMATIONS 107
5.3 TOTAL DUAL INTEGRALITY 109
5.4 TOTALLY UNIMODULAR MATRICES 112
5.5 CUTTING PLANES 117
5.6 LAGRANGEAN RELAXATION 121
EXERCISES 123
REFERENCES 127
6 SPANNING TREES AND ARBORESCENCES 131
6.1 MINIMUM SPANNING TREES 131
6.2 MINIMUM WEIGHT ARBORESCENCES 138
6.3 POLYHEDRAL DESCRIPTIONS 142
6.4 PACKING SPANNING TREES AND ARBORESCENCES 145
EXERCISES 148
REFERENCES 153
7 SHORTEST PATHS 157
7.1 SHORTEST PATHS FROM ONE SOURCE 158
7.2 SHORTEST PATHS BETWEEN ALL PAIRS OF VERTICES 162
7.3 MINIMUM MEAN CYCLES 165
EXERCISES 167
REFERENCES 169
8 NETWORK FLOWS 173
8.1 MAX-FLOW-MIN-CUT THEOREM 174
8.2 MENGER'S THEOREM 178
8.3 THE EDMONDS-KARP ALGORITHM 180
8.4 DINIC'S, KARZANOV'S, AND FUJISHIGE'S ALGORITHM 182
8.5 THE GOLDBERG-TARJAN ALGORITHM 186
8.6 GOMORY-HU TREES 190
8.7 THE MINIMUM CAPACITY OF A CUT IN AN UNDIRECTED GRAPH 196 EXERCISES
199
REFERENCES 205
9 MINIMUM COST FLOWS 211
9.1 PROBLEM FORMULATION 211
9.2 AN OPTIMALITY CRITERION 214
9.3 MINIMUM MEAN CYCLE-CANCELLING ALGORITHM 216
9.4 SUCCESSIVE SHORTEST PATH ALGORITHM 219
9.5 ORLIN'S ALGORITHM 223
9.6 THE NETWORK SIMPLEX ALGORITHM 227
9.7 FLOWS OVER TIME 231
EXERCISES 233
REFERENCES 237
IMAGE 3
TABLE OF CONTENTS XVII
10 MAXIMUM MATCHINGS 241
10.1 BIPARTITE MATCHING 242
10.2 THE TUTTE MATRIX 244
10.3 TUTTE'S THEOREM 246
10.4 EAR-DECOMPOSITIONS OF FACTOR-CRITICAL GRAPHS 249
10.5 EDMONDS' MATCHING ALGORITHM 255
EXERCISES 264
REFERENCES 268
11 WEIGHTED MATCHING 273
11.1 THE ASSIGNMENT PROBLEM 274
11.2 OUTLINE OF THE WEIGHTED MATCHING ALGORITHM 276
11.3 IMPLEMENTATION OF THE WEIGHTED MATCHING ALGORITHM 279 11.4
POSTOPTIMALITY 292
11.5 THE MATCHING POLYTOPE 293
EXERCISES 296
REFERENCES 298
12 O-MATCHINGS AND 7-JOINS 301
12.1 E-MATCHINGS 301
12.2 MINIMUM WEIGHT 7/-JOINS 305
12.3 R-JOINS AND 7/-CUTS 309
12.4 THE PADBERG-RAO THEOREM 313
EXERCISES 315
REFERENCES 318
13 MATROIDS 321
13.1 INDEPENDENCE SYSTEMS AND MATROIDS 321
13.2 OTHER MATROID AXIOMS 325
13.3 DUALITY 329
13.4 THE GREEDY ALGORITHM 333
13.5 MATROID INTERSECTION 338
13.6 MATROID PARTITIONING 343
13.7 WEIGHTED MATROID INTERSECTION 345
EXERCISES 349
REFERENCES 351
14 GENERALIZATIONS OF MATROIDS 355
14.1 GREEDOIDS 355
14.2 POLYMATROIDS 359
14.3 MINIMIZING SUBMODULAR FUNCTIONS 363
14.4 SCHRIJVER'S ALGORITHM 365
14.5 SYMMETRIC SUBMODULAR FUNCTIONS 369
EXERCISES 371
REFERENCES 374
IMAGE 4
XVIII TABLE OF CONTENTS
15 AT-COMPLETENESS 377
15.1 TURING MACHINES 377
15.2 CHURCH'S THESIS 380
15.3 F AND AFP 385
15.4 COOK'S THEOREM 389
15.5 SOME BASIC NP-COMPLETE PROBLEMS 392
15.6 THE CLASS CONP 400
15.7 ATP-HARD PROBLEMS 402
EXERCISES 406
REFERENCES 410
16 APPROXIMATION ALGORITHMS 413
16.1 SET COVERING 414
16.2 THE MAX-CUT PROBLEM 419
16.3 COLOURING 425
16.4 APPROXIMATION SCHEMES 433
16.5 MAXIMUM SATISFIABILITY 435
16.6 THEPCPTHEOREM 440
16.7 L-REDUCTIONS 444
EXERCISES 450
REFERENCES 454
17 THE KNAPSACK PROBLEM 459
17.1 FRACTIONAL KNAPSACK AND WEIGHTED MEDIAN PROBLEM 459 17.2 A
PSEUDOPOLYNOMIAL ALGORITHM 462
17.3 A FULLY POLYNOMIAL APPROXIMATION SCHEME 464
17.4 MULTI-DIMENSIONAL KNAPSACK 467
EXERCISES 468
REFERENCES 469
18 BIN-PACKING 471
18.1 GREEDY HEURISTICS 471
18.2 AN ASYMPTOTIC APPROXIMATION SCHEME 477
18.3 THE KARMARKAR-KARP ALGORITHM 481
EXERCISES 484
REFERENCES 486
19 MULTICOMMODITY FLOWS AND EDGE-DISJOINT PATHS 489
19.1 MULTICOMMODITY FLOWS 490
19.2 ALGORITHMS FOR MULTICOMMODITY FLOWS 494
19.3 SPARSEST CUT AND MAX-FLOW MIN-CUT RATIO 499
19.4 THE LEIGHTON-RAO THEOREM 500
19.5 DIRECTED EDGE-DISJOINT PATHS PROBLEM 503
19.6 UNDIRECTED EDGE-DISJOINT PATHS PROBLEM 507
EXERCISES 513
REFERENCES 517
IMAGE 5
TABLE OF CONTENTS XIX
20 NETWORK DESIGN PROBLEMS 521
20.1 STEINER TREES 522
20.2 THE ROBINS-ZELIKOVSKY ALGORITHM 527
20.3 SURVIVABLE NETWORK DESIGN 532
20.4 A PRIMAL-DUAL APPROXIMATION ALGORITHM 536
20.5 JAIN'S ALGORITHM 544
EXERCISES 550
REFERENCES 553
21 THE TRAVELING SALESMAN PROBLEM 557
21.1 APPROXIMATION ALGORITHMS FOR THE TSP 557
21.2 EUCLIDEAN TSP 562
21.3 LOCAL SEARCH 569
21.4 THE TRAVELING SALESMAN POLYTOPE 575
21.5 LOWER BOUNDS 581
21.6 BRANCH-AND-BOUND 584
EXERCISES 586
REFERENCES 589
22 FACILITY LOCATION 593
22.1 THE UNCAPACITATED FACILITY LOCATION PROBLEM 593
22.2 ROUNDING LINEAR PROGRAMMING SOLUTIONS 595
22.3 PRIMAL-DUAL ALGORITHMS 597
22.4 SCALING AND GREEDY AUGMENTATION 603
22.5 BOUNDING THE NUMBER OF FACILITIES 606
22.6 LOCAL SEARCH 609
22.7 CAPACITATED FACILITY LOCATION PROBLEMS 615
22.8 UNIVERSAL FACILITY LOCATION 618
EXERCISES 624
REFERENCES 626
NOTATION INDEX 629
AUTHOR INDEX 633
SUBJECT INDEX 645 |
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| dewey-full | 519.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.64 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 5. ed. |
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| spelling | Korte, Bernhard 1938- Verfasser (DE-588)139321802 aut Combinatorial optimization theory and algorithms Bernhard Korte ; Jens Vygen 5. ed. Berlin ; Heidelberg Springer 2012 XIX, 659 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics 21 Literaturangaben Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 s DE-604 Vygen, Jens 1967- Verfasser (DE-588)14204086X aut Algorithms and combinatorics 21 (DE-604)BV000617357 21 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3905406&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024841449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Korte, Bernhard 1938- Vygen, Jens 1967- Combinatorial optimization theory and algorithms Algorithms and combinatorics Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| subject_GND | (DE-588)4031826-6 |
| title | Combinatorial optimization theory and algorithms |
| title_auth | Combinatorial optimization theory and algorithms |
| title_exact_search | Combinatorial optimization theory and algorithms |
| title_full | Combinatorial optimization theory and algorithms Bernhard Korte ; Jens Vygen |
| title_fullStr | Combinatorial optimization theory and algorithms Bernhard Korte ; Jens Vygen |
| title_full_unstemmed | Combinatorial optimization theory and algorithms Bernhard Korte ; Jens Vygen |
| title_short | Combinatorial optimization |
| title_sort | combinatorial optimization theory and algorithms |
| title_sub | theory and algorithms |
| topic | Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| topic_facet | Kombinatorische Optimierung |
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