Combinatorial optimization: theory and algorithms
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Edition: | 3. ed. |
| Series: | Algorithms and combinatorics
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 597 S. Ill., graph. Darst. |
| ISBN: | 3540256849 9783540256847 |
Staff View
MARC
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| 245 | 1 | 0 | |a Combinatorial optimization |b theory and algorithms |c Bernhard Korte ; Jens Vygen |
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Record in the Search Index
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| adam_text |
BERNHARD KORTE JENS VYGEN COMBINATORIAL OPTIMIZATION THEORY AND
ALGORITHMS THIRD EDITION 4Y 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 90 XII TABLE OF CONTENTS 5. INTEGER PROGRAMMING
91 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 119 6.1
MINIMUM SPANNING TREES 119 6.2 MINIMUM WEIGHT ARBORESCENCES 125 6.3
POLYHEDRAL DESCRIPTIONS 129 6.4 PACKING SPANNING TREES AND ARBORESCENCES
132 EXERCISES 136 REFERENCES 139 7. SHORTEST PATHS 143 7.1 SHORTEST
PATHS FROM ONE SOURCE 144 7.2 SHORTEST PATHS BETWEEN ALL PAIRS OF
VERTICES 148 7.3 MINIMUM MEAN CYCLES 151 EXERCISES 153 REFERENCES 155 8.
NETWORK FLOWS 157 8.1 MAX-FLOW-MIN-CUT THEOREM 158 8.2 MENGER'S THEOREM
162 8.3 THE EDMONDS-KARP ALGORITHM 164 8.4 BLOCKING FLOWS AND
FUJISHIGE'S ALGORITHM 166 8.5 THE GOLDBERG-TARJAN ALGORITHM 168 8.6
GOMORY-HU TREES 172 8.7 THE MINIMUM CUT IN AN UNDIRECTED GRAPH 179
EXERCISES 181 REFERENCES 186 9. MINIMUM COST FLOWS 191 9.1 PROBLEM
FORMULATION 191 9.2 AN OPTIMALITY CRITERION 193 9.3 MINIMUM MEAN
CYCLE-CANCELLING ALGORITHM 195 9.4 SUCCESSIVE SHORTEST PATH ALGORITHM
199 9.5 ORLIN'S ALGORITHM 203 9.6 FLOWS OVER TIME 206 EXERCISES 208
REFERENCES 212 TABLE OF CONTENTS XIII 10. MAXIMUM MATCHINGS 215 10.1
BIPARTITE MATCHING 216 10.2 THE TUTTE MATRIX 218 10.3 TUTTE'S THEOREM
220 10.4 EAR-DECOMPOSITIONS OF FACTOR-CRITICAL GRAPHS 223 10.5 EDMONDS'
MATCHING ALGORITHM 229 EXERCISES 238 REFERENCES 242 11. WEIGHTED
MATCHING 245 11.1 THE ASSIGNMENT PROBLEM 246 11.2 OUTLINE OF THE
WEIGHTED MATCHING ALGORITHM 247 11.3 IMPLEMENTATION OF THE WEIGHTED
MATCHING ALGORITHM 250 11.4 POSTOPTIMALITY 263 11.5 THE MATCHING
POLYTOPE 264 EXERCISES 267 REFERENCES 269 12. 6-MATCHINGS AND T-JOINS
271 12.1 FC-MATCHINGS 271 12.2 MINIMUM WEIGHT R -JOINS 275 12.3 T-JOINS
AND T-CUTS 279 12.4 THE PADBERG-RAO THEOREM 282 EXERCISES 285 REFERENCES
288 13. MATROIDS 291 13.1 INDEPENDENCE SYSTEMS AND MATROIDS 291 13.2
OTHER MATROID AXIOMS 295 13.3 DUALITY 299 13.4 THE GREEDY ALGORITHM 303
13.5 MATROID INTERSECTION 308 13.6 MATROID PARTITIONING 313 13.7
WEIGHTED MATROID INTERSECTION 314 EXERCISES 318 REFERENCES 320 14.
GENERALIZATIONS OF MATROIDS 323 14.1 GREEDOIDS 323 14.2 POLYMATROIDS 327
14.3 MINIMIZING SUBMODULAR FUNCTIONS 331 14.4 SCHRIJVER'S ALGORITHM 333
14.5 SYMMETRIC SUBMODULAR FUNCTIONS 337 EXERCISES 339 REFERENCES 341 XIV
TABLE OF CONTENTS 15. NP -COMPLETENESS 343 15.1 TURING MACHINES 343 15.2
CHURCH'S THESIS 345 15.3 P AND JVP 350 15.4 COOK'S THEOREM 354 15.5 SOME
BASIC NP -COMPLETE PROBLEMS 358 15.6 THE CLASS CONP 365 15.7 M -HARD
PROBLEMS 367 EXERCISES 371 REFERENCES 374 16. APPROXIMATION ALGORITHMS
377 16.1 SET COVERING 378 16.2 COLOURING 383 16.3 APPROXIMATION SCHEMES
390 16.4 MAXIMUM SATISFIABILITY 392 16.5 THE PCP THEOREM 397 16.6
L-REDUCTIONS 401 EXERCISES 407 REFERENCES 410 17. THE KNAPSACK PROBLEM
415 17.1 FRACTIONAL KNAPSACK AND WEIGHTED MEDIAN PROBLEM 415 17.2 A
PSEUDOPOLYNOMIAL ALGORITHM 418 17.3 A FULLY POLYNOMIAL APPROXIMATION
SCHEME 420 EXERCISES 422 REFERENCES 423 18. BIN-PACKING 425 18.1 GREEDY
HEURISTICS 425 18.2 AN ASYMPTOTIC APPROXIMATION SCHEME 431 18.3 THE
KARMARKAR-KARP ALGORITHM 435 EXERCISES 438 REFERENCES 439 19.
MULTICOMMODITY FLOWS AND EDGE-DISJOINT PATHS 443 19.1 MULTICOMMODITY
FLOWS 444 19.2 ALGORITHMS FOR MULTICOMMODITY FLOWS 447 19.3 DIRECTED
EDGE-DISJOINT PATHS PROBLEM 451 19.4 UNDIRECTED EDGE-DISJOINT PATHS
PROBLEM 455 EXERCISES 460 REFERENCES 463 TABLE OF CONTENTS XV 20.
NETWORK DESIGN PROBLEMS 467 20.1 STEINER TREES 468 20.2 THE
ROBINS-ZELIKOVSKY ALGORITHM 473 20.3 SURVIVABLE NETWORK DESIGN 478 20.4
A PRIMAL-DUAL APPROXIMATION ALGORITHM 481 20.5 JAIN'S ALGORITHM 489
EXERCISES 495 REFERENCES 498 21. THE TRAVELING SALESMAN PROBLEM 501 21.1
APPROXIMATION ALGORITHMS FOR THE TSP 501 21.2 EUCLIDEAN TSPS 506 21.3
LOCAL SEARCH 513 21.4 THE TRAVELING SALESMAN POLYTOPE 519 21.5 LOWER
BOUNDS 525 21.6 BRANCH-AND-BOUND 527 EXERCISES 530 REFERENCES 532 22.
FACILITY LOCATION 537 22.1 THE UNCAPACITATED FACILITY LOCATION PROBLEM
537 22.2 ROUNDING LINEAR PROGRAMMING SOLUTIONS 539 22.3 PRIMAL-DUAL
ALGORITHMS 541 22.4 SCALING AND GREEDY AUGMENTATION 547 22.5 BOUNDING
THE NUMBER OF FACILITIES 550 22.6 LOCAL SEARCH 553 22.7 CAPACITATED
FACILITY LOCATION PROBLEMS 559 22.8 UNIVERSAL FACILITY LOCATION 561
EXERCISES 568 REFERENCES 570 NOTATION INDEX 573 AUTHOR INDEX 577 SUBJECT
INDEX 585 |
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| author | Korte, Bernhard Vygen, Jens 1967- |
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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 |
| dewey-search | 519.64 |
| dewey-sort | 3519.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-20T07:20:20Z |
| institution | BVB |
| isbn | 3540256849 9783540256847 |
| language | English |
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| physical | XV, 597 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| 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 3. ed. Berlin [u.a.] Springer 2006 XV, 597 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics 21 Kombinatorische Optimierung - Lehrbuch 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=013362065&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 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 Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| topic_facet | Kombinatorische Optimierung - Lehrbuch Kombinatorische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013362065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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