Combinatorial optimization: theory and algorithms
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Algorithms and combinatorics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 530 S. Ill., graph. Darst. |
| ISBN: | 3540431543 |
Internformat
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| 245 | 1 | 0 | |a Combinatorial optimization |b theory and algorithms |c Bernhard Korte ; Jens Vygen |
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Datensatz im Suchindex
| _version_ | 1804129012277051392 |
|---|---|
| adam_text | BERNHARD KORTE JENS VYGEN COMBINATORIAL OPTIMIZATION THEORY AND
ALGORITHMS SECOND EDITION SPRINGER TABLE OF CONTENTS 1. 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 2.
GRAPHS 13 2.1 BASIC DEFINITIONS 13 2.2 TREES, CIRCUITS, AND CUTS 17 2.3
CONNECTIVITY 24 2.4 EULERIAN AND BIPARTITE GRAPHS 30 2.5 PLANARITY 33
2.6 PLANAR DUALITY 40 EXERCISES 42 REFERENCES 46 3. LINEAR PROGRAMMING
49 3.1 POLYHEDRA 50 3.2 THE SIMPLEX ALGORITHM 53 3.3 DUALITY 57 3.4
CONVEX HULLS AND POLYTOPES 60 EXERCISES 62 REFERENCES 63 4. LINEAR
PROGRAMMING ALGORITHMS 65 4.1 SIZE OF VERTICES AND FACES 65 4.2
CONTINUED FRACTIONS 68 4.3 GAUSSIAN ELIMINATION 70 4.4 THE ELLIPSOID
METHOD 74 4.5 KHACHIYAN S THEOREM 80 4.6 SEPARATION AND OPTIMIZATION 82
EXERCISES 88 REFERENCES 89 X TABLE OF CONTENTS 5. INTEGER PROGRAMMING 9
1 5.1 THE INTEGER HULL OF A POLYHEDRON 92 5.2 UNIMODULAR TRANSFORMATIONS
96 5.3 TOTAL DUAL INTEGRALITY 97 5.4 TOTALLY UNIMODULAR MATRICES 101 5.5
CUTTING PLANES 106 5.6 LAGRANGEAN RELAXATION 110 EXERCISES 112
REFERENCES 115 6. SPANNING TREES AND ARBORESCENCES 117 6.1 MINIMUM
SPANNING TREES 118 6.2 MINIMUM WEIGHT ARBORESCENCES 121 6.3 POLYHEDRAL
DESCRIPTIONS 125 6.4 PACKING SPANNING TREES AND ARBORESCENCES 128
EXERCISES 132 REFERENCES 135 7. SHORTEST PATHS 139 7.1 SHORTEST PATHS
FROM ONE SOURCE 140 7.2 SHORTEST PATHS BETWEEN ALL PAIRS OF VERTICES 144
7.3 MINIMUM MEAN CYCLES 147 EXERCISES 149 REFERENCES 151 8. NETWORK
FLOWS 153 8.1 MAX-FLOW-MIN-CUT THEOREM 154 I 8.2 MENGER S THEOREM 158 I
8.3 THE EDMONDS-KARP ALGORITHM 160 1 8.4 BLOCKING FLOWS 162 I 8.5 THE
GOLDBERG-TARJAN ALGORITHM 163 8.6 GOMORY-HU TREES 168 *} 8.7 THE MINIMUM
CUT IN AN UNDIRECTED GRAPH 174 EXERCISES 176 I REFERENCES 181 J | 9.
MINIMUM COST FLOWS 185 J 9.1 PROBLEM FORMULATION 185 5 9.2 AN OPTIMALITY
CRITERION 187 ; 9.3 MINIMUM MEAN CYCLE-CANCELLING ALGORITHM 189 1 9.4
SUCCESSIVE SHORTEST PATH ALGORITHM 193 ] 9.5 ORLIN S ALGORITHM 197 I
EXERCISES 201 I REFERENCES 203 TABLE OF CONTENTS XI 10. MAXIMUM
MATCHINGS 205 10.1 BIPARTITE MATCHING 206 10.2 THE TUTTE MATRIX 208 10.3
TUTTE S THEOREM 210 10.4 EAR-DECOMPOSITIONS OF FACTOR-CRITICAL GRAPHS
213 10.5 EDMONDS MATCHING ALGORITHM 219 EXERCISES 228 REFERENCES 231
11. WEIGHTED MATCHING 235 11.1 THE ASSIGNMENT PROBLEM 236 11.2 OUTLINE
OF THE WEIGHTED MATCHING ALGORITHM 237 11.3 IMPLEMENTATION OF THE
WEIGHTED MATCHING ALGORITHM 240 11.4 POSTOPTIMALITY 253 11.5 THE
MATCHING POLYTOPE 254 EXERCISES 257 REFERENCES 259 12. Z»-MATCHINGS AND
T -JOINS 261 12.1 FO-MATCHINGS 261 12.2 MINIMUM WEIGHT 7 -JOINS 265 12.3
R -JOINS AND T-CUTS 269 12.4 THE PADBERG-RAO THEOREM 272 EXERCISES 275
REFERENCES 278 13. MATROIDS 279 13.1 INDEPENDENCE SYSTEMS AND MATROIDS
279 13.2 OTHER MATROID AXIOMS 283 13.3 DUALITY 287 13.4 THE GREEDY
ALGORITHM 291 13.5 MATROID INTERSECTION 296 13.6 MATROID PARTITIONING
300 13.7 WEIGHTED MATROID INTERSECTION 302 EXERCISES 305 REFERENCES 308
14. GENERALIZATIONS OF MATROIDS 31 1 14.1 GREEDOIDS 311 14.2
POLYMATROIDS 315 14.3 MINIMIZING SUBMODULAR FUNCTIONS 319 EXERCISES 323
REFERENCES 325 XII TABLE OF CONTENTS 15. NP -COMPLETENESS 327 15.1
TURING MACHINES 327 15.2 CHURCH S THESIS 329 15.3 P AND NP 334 15.4
COOK S THEOREM 338 15.5 SOME BASIC NP-COMPLETE PROBLEMS 342 15.6 THE
CLASS CONP 349 15.7 NP-HARD PROBLEMS 351 EXERCISES 354 REFERENCES 358
16. APPROXIMATION ALGORITHMS 361 16.1 SET COVERING 362 16.2 COLOURING
367 16.3 APPROXIMATION SCHEMES 373 16.4 MAXIMUM SATISFIABILITY 376 16.5
THE PCP THEOREM 380 16.6 L-REDUCTIONS 384 EXERCISES 390 REFERENCES 393
17. THE KNAPSACK PROBLEM 397 17.1 FRACTIONAL KNAPSACK AND WEIGHTED
MEDIAN PROBLEM 397 17.2 A PSEUDOPOLYNOMIAL ALGORITHM 400 17.3 A FULLY
POLYNOMIAL APPROXIMATION SCHEME 402 EXERCISES 405 REFERENCES 406 18.
BIN-PACKING 407 18.1 GREEDY HEURISTICS 407 18.2 AN ASYMPTOTIC
APPROXIMATION SCHEME 412 18.3 THE KARMARKAR-KARP ALGORITHM 416 EXERCISES
419 REFERENCES 421 19. MULTICOMMODITY FLOWS AND EDGE-DISJOINT PATHS 423
19.1 MULTICOMMODITY FLOWS 424 19.2 ALGORITHMS FOR MULTICOMMODITY FLOWS
427 19.3 DIRECTED EDGE-DISJOINT PATHS PROBLEM 431 19.4 UNDIRECTED
EDGE-DISJOINT PATHS PROBLEM 435 EXERCISES 440 REFERENCES 443 TABLE OF
CONTENTS XIII 20. NETWORK DESIGN PROBLEMS 445 20.1 STEINER TREES 446
20.2 SURVIVABLE NETWORK DESIGN 450 20.3 A PRIMAL-DUAL APPROXIMATION
ALGORITHM 453 20.4 JAIN S ALGORITHM 462 EXERCISES 467 REFERENCES 470 21.
THE TRAVELING SALESMAN PROBLEM 473 21.1 APPROXIMATION ALGORITHMS FOR THE
TSP 473 21.2 EUCLIDEAN TSPS 478 21.3 LOCAL SEARCH 485 21.4 THE TRAVELING
SALESMAN POLYTOPE 491 21.5 LOWER BOUNDS 497 21.6 BRANCH-AND-BOUND 499
EXERCISES 501 REFERENCES 503 NOTATION INDEX 507 AUTHOR INDEX 511 SUBJECT
INDEX 519
|
| any_adam_object | 1 |
| author | Korte, Bernhard Vygen, Jens 1967- |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)248749202 (DE-599)BVBBV014140435 |
| dewey-full | 519.321 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 21 519.3 |
| dewey-search | 519.3 21 519.3 |
| dewey-sort | 3519.3 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:58:22Z |
| institution | BVB |
| isbn | 3540431543 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009689740 |
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| physical | XIII, 530 S. Ill., graph. Darst. |
| publishDate | 2002 |
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| publisher | Springer |
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| series | Algorithms and combinatorics |
| series2 | Algorithms and combinatorics |
| spelling | Korte, Bernhard Verfasser aut Combinatorial optimization theory and algorithms Bernhard Korte ; Jens Vygen 2. ed. Berlin [u.a.] Springer 2002 XIII, 530 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics 21 Kombinatorische Optimierung - Lehrbuch Combinatorial optimization 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 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009689740&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Korte, Bernhard Vygen, Jens 1967- Combinatorial optimization theory and algorithms Algorithms and combinatorics Kombinatorische Optimierung - Lehrbuch Combinatorial optimization 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 - Lehrbuch Combinatorial optimization Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| topic_facet | Kombinatorische Optimierung - Lehrbuch Combinatorial optimization Kombinatorische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009689740&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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