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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| 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_ | 1824928736289488896 |
|---|---|
| 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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| 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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| id | DE-604.BV044722203 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-24T09:01:04Z |
| institution | BVB |
| isbn | 9783662560389 |
| language | English |
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| physical | XXI, 698 Seiten Diagramme 25 cm |
| publishDate | 2018 |
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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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