Combinatorial optimization: theory and algorithms
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2018]
|
| Ausgabe: | sixth edition |
| Schriftenreihe: | Algorithms and combinatorics
volume 21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XXI, 698 Seiten Diagramme 25 cm |
| ISBN: | 9783662560389 |
Internformat
MARC
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| 100 | 1 | |a Korte, Bernhard |d 1938- |0 (DE-588)139321802 |4 aut | |
| 245 | 1 | 0 | |a Combinatorial optimization |b theory and algorithms |c Bernhard Korte, Jens Vygen |
| 250 | |a sixth edition | ||
| 264 | 1 | |a Berlin |b Springer |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a XXI, 698 Seiten |b Diagramme |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Vygen, Jens |d 1967- |0 (DE-588)14204086X |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-662-56039-6 |
| 830 | 0 | |a Algorithms and combinatorics |v volume 21 |w (DE-604)BV000617357 |9 21 | |
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Datensatz im Suchindex
| _version_ | 1804178211085484032 |
|---|---|
| adam_text | 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 ..................................................................................................... 2.1 Basic Definitions ............................................................................. 2.2 Trees, Circuits, and Cuts ................................................................ 2.3 Connectivity .................................................................................... 2.4 Eulerian and Bipartite Graphs ........................................................ 2.5 Planarity .......................................................................................... 2.6 Planar Duality ................................................................................. Exercises....................................................................................................
References............................................................................................. 15 15 19 26 33 36 43 46 49 3 Linear Programming ............................................................................. 3.1 Polyhedra ........................................................................................ 3.2 The Simplex Algorithm .................................................................. 3.3 Implementation of the Simplex Algorithm .................................... 3.4 Duality ............................................................................................ 3.5 Convex Hulls and Poly topes .......................................................... Exercises.................................................................................................... References.................................................................................................. 53 54 58 62 65 69 70 72 4 Linear Programming Algorithms ........................................................ 4.1 Size of Vertices and Faces .............................................................. 4.2 Continued Fractions ....................................................................... 4.3 Gaussian Elimination ..................................................................... 4.4 The Ellipsoid Method ..................................................................... 4.5 Khachiyan’s Theorem....................................................................... 75 75 78 81 84 90 XVII
XVIII Table of Contents 4.6 Separation and Optimization .......................................................... 93 Exercises.................................................................................................... 99 References................................................................................................... 101 5 Integer Programming...............................................................................103 5.1 The Integer Hull of a Polyhedron.....................................................105 5.2 Unimodular Transformations ............................................................ 109 5.3 Total Dual Integrality ....................................................................... Ill 5.4 Totally Unimodular Matrices ............................................................ 115 5.5 Cutting Planes ...................................................................................120 5.6 Lagrangean Relaxation ......................................................................124 Exercises..................................................................................................... 126 References....................................................................................................129 6 Spanning TVees and Arborescences .......................................................133 6.1 Minimum Spanning Trees ................................................................ 134 6.2 Minimum Weight Arborescences .....................................................140 6.3 Polyhedral Descriptions
....................................................................144 6.4 Packing Spanning Trees and Arborescences ....................................147 Exercises..................................................................................................... 151 References................................................................................................... 155 7 Shortest Paths .......................................................................................... 159 7.1 Shortest Paths From One Source .....................................................160 7.2 Shortest Paths Between All Pairsof Vertices ................................... 165 7.3 Minimum Mean Cycles ....................................................................167 7.4 Shallow-Light Trees ......................................................................... 169 Exercises..................................................................................................... 171 References....................................................................................................173 8 Network Flows.......................................................................................... 177 8.1 Max-Flow-Min-Cut Theorem .......................................................... 178 8.2 Menger’s Theorem............................................................................. 182 8.3 The Edmonds-Karp Algorithm.......................................................... 184 8.4 Dime’s, Karzanov’s, and Fujishige’s Algorithm................................186 8.5 The
Goldberg-Tarjan Algorithm........................................................ 190 8.6 Gomory-Hu Trees...............................................................................194 8.7 The Minimum Capacity of a Cut in an Undirected Graph........... 201 Exercises..................................................................................................... 203 References................................................................................................... 210 9 Minimum Cost Flows...............................................................................215 9.1 Problem Formulation ....................................................................... 215 9.2 An Optimality Criterion ............................................... 218 9.3 Minimum Mean Cycle-Cancelling Algorithm................................. 220 9.4 Successive Shortest Path Algorithm .................................................223 9.5 Orlin’s Algorithm.............................................................................. 227
Table of Contents XIX 9.6 The Network Simplex Algorithm .................................................... 232 9.7 Flows Over Time............................. 236 Exercises.....................................................................................................238 References................................................................................................... 241 10 Maximum Matchings .................................................... 245 10.1 Bipartite Matching .......................................................................... 246 10.2 The Tutte Matrix............................................................... 248 10.3 Tutte’s Theorem................................................................................ 250 10.4 Ear-Decompositions of Factor-Critical Graphs ............................... 253 10.5 Edmonds’ Matching Algorithm........................................................259 Exercises................................................................... 269 References................................................................................................... 273 11 Weighted Matching.................................................................................. 277 11.1 The Assignment Problem ................................................................. 278 11.2 Outline of the Weighted Matching Algorithm ............................... 280 11.3 Implementation of the Weighted Matching Algorithm .................. 283 11.4 Postoptimality
.................................................................................. 296 11.5 The Matching Polytope ................................................................... 297 Exercises...................................................................................... 300 References................................................................... 302 12 ¿-Matchings and Г-Joins.........................................................................305 12.1 ¿-Matchings........................................................................................305 12.2 Minimum Weight Г-Joins................................................................. 309 12.3 Г-Joins and Г-Cuts.......................................................................... 313 12.4 The Padberg-Rao Theorem.......................... 317 Exercises............................................................................................. 319 References................................................................................................... 323 13 Matroids ...................................................................................................325 13.1 Independence Systems and Matroids .............................................. 325 13.2 Other Matroid Axioms .....................................................................329 13.3 Duality ............................................................................................. 334 13.4 The Greedy Algorithm .....................................................................337 13.5 Matroid Intersection
.........................................................................343 13.6 Matroid Partitioning .........................................................................347 13.7 Weighted Matroid Intersection ........................................................349 Exercises................................................................... 353 References......................................... 355 14 Generalizations of Matroids ................................................................... 359 14.1 Greedoids ......................................................................................... 359 14.2 Polymatroids .................................................................................... 363 14.3 Minimizing Submodular Functions.................................................. 367 14.4 Schrijver’s Algorithm .......................................................................370
XX Table of Contents 14.5 Symmetric Submodular Functions ............................ 14.6 Submodular Function Maximization.......................... Exercises.................................................................................. References................................................................................ 15 AP-Completeness.................................................................. 15.1 Tbring Machines............................................................ 15.2 Church’s Thesis.............................................................. 15.3 P and NP........................................................................ 15.4 Cook’s Theorem............................................................ 15.5 Some Basic №P-Complete Problems.......................... 15.6 The Class coNP............................................................ 15.7 AP-Hard Problems........................................................ Exercises.................................................................................. References................................................................................ 16 Approximation Algorithms ................................................ 16.1 Set Covering ................................................................ 16.2 The Max-Cut Problem ................................................ 16.3 Colouring ...................................................................... 16.4 Approximation Schemes.............................................. 16.5 Maximum Satisfiability
.............................................. 16.6 The PCP Theorem........................................................ 16.7 L-Reductions.................................................................. Exercises.................................................................................. References................................................................................ 17 The Knapsack Problem ...................................................... 17.1 Fractional Knapsack and Weighted Median Problem 17.2 A Pseudopolynomial Algorithm ................................ 17.3 A Fully Polynomial Approximation Scheme .......... 17.4 Multi-Dimensional Knapsack .................................... 17.5 The Nemhauser-Ullmann Algorithm.......................... Exercises.................................................................................. References................................................................................ 18 Bin-Packing .......................................................................... 18.1 Greedy Heuristics ........................................................ 18.2 An Asymptotic Approximation Scheme .................. 18.3 The Karmarkar-Karp Algorithm.................................. Exercises.................................................................................. References................................................................................ 19 Multicommodity Flows and Edge-Disjoint Paths ........ 19.1 Multicommodity Flows................................................ 19.2 Algorithms for
Multicommodity Flows .................... 19.3 Sparsest Cut and Max-Flow Min-Cut Ratio ............
Table of Contents XXI 19.4 The Leighton-Rao Theorem............................................................. 521 19.5 Directed Edge-Disjoint Paths Problem............................................ 524 19.6 Undirected Edge-Disjoint Paths Problem.........................................527 Exercises.....................................................................................................533 References...................................................................................................537 20 Network Design Problems.......................................................................543 20.1 Steiner Trees ....................................................................................544 20.2 The Robins-Zelikovsky Algorithm....................................................549 20.3 Rounding the Directed Component LP ...........................................555 20.4 Survivable Network Design ............................................................. 561 20.5 A Primal-Dual Approximation Algorithm .......................................564 20.6 Jain’s Algorithm................................................................................ 572 20.7 The VPN Problem............................................................................ 578 Exercises.....................................................................................................581 References...................................................................................................585 21 The Traveling Salesman Problem
......................................................... 591 21.1 Approximation Algorithms for the TSP .........................................591 21.2 Euclidean TSP .................................................................................. 596 21.3 Local Search ....................................................................................603 21.4 The Traveling Salesman Poly tope.................................................... 610 21.5 Lower Bounds .................................................................................. 616 21.6 Branch-and-Bound............................................................................ 618 Exercises.....................................................................................................621 References.................................................................................. 624 22 Facility Location ......................................................................................629 22.1 The Uncapacitated Facility Location Problem ............................... 629 22.2 Rounding Linear Programming Solutions .......................................631 22.3 Primal-Dual Algorithms ...................................................................633 22.4 Scaling and Greedy Augmentation....................................................639 22.5 Bounding the Number of Facilities.................................................. 642 22.6 Local Search ....................................................................................645 22.7 Capacitated Facility Location
Problems...........................................651 • 22.8 Universal Facility Location ............................................................. 654 Exercises.....................................................................................................661 References...................................................................................................662 Notation Index...................................................................................................667 Author Index.....................................................................................................671 Subject Index............................... 683
|
| any_adam_object | 1 |
| author | Korte, Bernhard 1938- Vygen, Jens 1967- |
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| author_role | aut aut |
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| author_variant | b k bk j v jv |
| building | Verbundindex |
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| classification_tum | MAT 913f |
| ctrlnum | (OCoLC)1020568382 (DE-599)BVBBV044722203 |
| 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 | sixth edition |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:00:21Z |
| institution | BVB |
| isbn | 9783662560389 |
| language | English |
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| physical | XXI, 698 Seiten Diagramme 25 cm |
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| series | Algorithms and combinatorics |
| series2 | Algorithms and combinatorics |
| spelling | Korte, Bernhard 1938- (DE-588)139321802 aut Combinatorial optimization theory and algorithms Bernhard Korte, Jens Vygen sixth edition Berlin Springer [2018] © 2018 XXI, 698 Seiten Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics volume 21 Literaturangaben Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 s DE-604 Vygen, Jens 1967- (DE-588)14204086X aut Erscheint auch als Online-Ausgabe 978-3-662-56039-6 Algorithms and combinatorics volume 21 (DE-604)BV000617357 21 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030118450&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 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030118450&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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