Verfügbarkeit: Combinatorial optimization | Technische Universität München

Combinatorial optimization: theory and algorithms

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Bibliographische Detailangaben
Beteiligte Personen:	Korte, Bernhard 1938- (VerfasserIn), Vygen, Jens 1967- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg Springer 2012
Ausgabe:	5. ed.
Schriftenreihe:	Algorithms and combinatorics 21
Schlagwörter:	Kombinatorische Optimierung
Links:	http://deposit.dnb.de/cgi-bin/dokserv?id=3905406&prov=M&dok_var=1&dok_ext=htm 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
Beschreibung:	Literaturangaben
Umfang:	XIX, 659 S. graph. Darst. 25 cm
ISBN:	9783642244872 3642244874 9783642244889

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Datensatz im Suchindex

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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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series	Algorithms and combinatorics
series2	Algorithms and combinatorics
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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