Holdings: Combinatorial optimization

Combinatorial optimization: theory and algorithms

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Bibliographic Details
Main Authors:	Korte, Bernhard (Author), Vygen, Jens 1967- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2002
Edition:	2. ed.
Series:	Algorithms and combinatorics 21
Subjects:	Kombinatorische Optimierung - Lehrbuch Combinatorial optimization Kombinatorische Optimierung
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 530 S. Ill., graph. Darst.
ISBN:	3540431543

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MARC


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Record in the Search Index

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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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edition	2. ed.
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series	Algorithms and combinatorics
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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
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