Complexity and approximation: combinatorial optimization problems and their approximability properties ; with 4 tables
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Edition: | 2., corr. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Teilw. ohne CD-ROM. - Additional material to this book can be downloaded from http://extras.springer.com |
| Physical Description: | XIX, 524 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 3540654313 9783540654315 |
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| 245 | 1 | 0 | |a Complexity and approximation |b combinatorial optimization problems and their approximability properties ; with 4 tables |c G. Ausiello ... |
| 250 | |a 2., corr. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XIX, 524 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Teilw. ohne CD-ROM. - Additional material to this book can be downloaded from http://extras.springer.com | ||
| 650 | 4 | |a Kombinatorische Optimierung - Komplexitätstheorie - NP-vollständiges Problem - Approximationsalgorithmus | |
| 650 | 4 | |a Combinatorial optimization | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Computer algorithms | |
| 650 | 0 | 7 | |a Komplexitätstheorie |0 (DE-588)4120591-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a NP-vollständiges Problem |0 (DE-588)4138229-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximationsalgorithmus |0 (DE-588)4500954-5 |2 gnd |9 rswk-swf |
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| adam_text | Contents
1
The Complexity of Optimization Problems
1
1.1
Analysis of algorithms and complexity of problems
.... 2
1.1.1
Complexity analysis of computer programs
.... 3
1.1.2
Upper and lower bounds on the complexity of
problems
...................... 8
1.2
Complexity classes of decision problems
.......... 9
1.2.1
The class NP
.................... 12
1.3
Reducibility among problems
................ 17
1.3.1
Karp
and Turing reducibility
............ 17
1.3.2
NP-complete problems
............... 21
1.4
Complexity of optimization problems
........... 22
1.4.1
Optimization problems
............... 22
1.4.2
PO
and NPO problems
............... 26
1.4.3
NP-hard optimization problems
.......... 29
1.4.4
Optimization problems and evaluation problems
. 31
1.5
Exercises
.......................... 33
1.6
Bibliographical notes
.................... 36
2
Design Techniques for Approximation Algorithms
39
2.1
The greedy method
..................... 40
2.1.1
Greedy algorithm for the knapsack problem
.... 41
2.1.2
Greedy algorithm for the independent set problem
43
2.1.3
Greedy algorithm for the salesperson problem
... 47
Table
of contents
2.2
Sequential algorithms for partitioning problems
...... 50
2.2.1
Scheduling jobs on identical machines
....... 51
2.2.2
Sequential algorithms for bin packing
....... 54
2.2.3
Sequential algorithms for the graph coloring problem
58
2.3
Local search
......................... 61
2.3.1
Local search algorithms for the cut problem
.... 62
2.3.2
Local search algorithms for the salesperson problem
64
2.4
Linear programming based algorithms
........... 65
2.4.1
Rounding the solution of a linear program
..... 66
2.4.2
Primal-dual algorithms
............... 67
2.5
Dynamic programming
................... 69
2.6
Randomized algorithms
................... 74
2.7
Approaches to the approximate solution of problems
... 76
2.7.1
Performance guarantee: chapters
3
and
4..... 76
2.7.2
Randomized algorithms: chapter
5......... 77
2.7.3
Probabilistic analysis: chapter
9.......... 77
2.7.4
Heuristics: chapter
10............... 78
2.7.5
Final remarks
.................... 79
2.8
Exercises
.......................... 79
2.9
Bibliographical notes
.................... 83
3
Approximation Classes
87
3.1
Approximate solutions with guaranteed performance
... 88
3.1.1
Absolute approximation
.............. 88
3.1.2
Relative approximation
............... 90
3.1.3
Approximability and non-approximability of TSP
. 94
3.1.4
Limits to approximability: The gap technique
. . . 100
3.2
Polynomial-time approximation schemes
.......... 102
3.2.1
The class PTAS
................... 105
3.2.2
APX versus PTAS
................. 110
3.3
Fully polynomial-time approximation schemes
......
Ill
3.3.1
The class FPTAS
..................
Ill
3.3.2
The variable partitioning technique
........ 112
3.3.3
Negative results for the class FPTAS
........ 113
3.3.4
Strong NP-completeness and pseudo-polynomiality
114
3.4
Exercises
.......................... 116
3.5
Bibliographical notes
.................... 119
4
Input-Dependent and Asymptotic Approximation
123
4.1
Between APX and NPO
................... 124
4.1.1
Approximating the set cover problem
....... 124
____ 4.1.2
Approximating the graph coloring problem
.... 127
VIII
.
,
- .
Table of contents
4.1.
і
Approximating the minimum multi-cut problem
. . 129 -------------------------
4.2
Between APX and PTAS
..................139
4.2.1
Approximating the edge coloring problem
..... 139
4.2.2
Approximating the bin packing problem
...... 143
4.3
Exercises
..........................
14g
4.4
Bibliographical notes
.................... 150
5
Approximation through Randomization
153
5.1
Randomized algorithms for weighted vertex cover
..... 154
5.2
Randomized algorithms for weighted satisfiability
..... 157
5.2.1
A new randomized approximation algorithm
... 157
5.2.2
A 4/3-approximation randomized algorithm
.... 160
5.3
Algorithms based on
semidefinite
programming
...... 162
5.3.1
Improved algorithms for weighted 2-satisfiability
. 167
5.4
The method of the conditional probabilities
........ 168
5.5
Exercises
.......................... 171
5.6
Bibliographical notes
.................... 173
6
NP,
PCP
and Non-approximability Results
175
6.1
Formal complexity theory
.................. 175
6.1.1
Turing machines
.................. 175
6.1.2
Deterministic Turing machines
........... 178
6.1.3
Nondeterministic Turing machines
......... 180
6.1.4
Time and space complexity
............. 181
6.1.5
NP-completeness and Cook-Levin theorem
.... 184
6.2
Oracles
........................... 188
6.2.1
Oracle Turing machines
.............. 189
6.3
The
PCP
model
....................... 190
6.3.1
Membership proofs
................. 190
6.3.2
Probabilistic Turing machines
........... 191
6.3.3
Verifiers and
PCP
.................. 193
6.3.4
A different view of
NP
............... 194
6.4
Using
PCP
to prove non-approximability results
...... 195
6.4.1
The maximum satisfiability problem
........ 196
6.4.2
The maximum clique problem
........... 198
6.5
Exercises
..........................
200
6.6
Bibliographical notes
.................... 204
7
The
PCP
theorem 207
7.1
Transparent long proofs
...................
208
7.1.1
Linear functions
..................
21°
7.1.2
Arithmetization
...................
214
------
IX
Table
of contents
------------------------- 7.1.3
The first
PCP
result
.................218
7.2
Almost transparent short proofs
...............221
7.2.1
Low-degree polynomials
.............. 222
7.2.2
Arithmetization (revisited)
............. 231
7.2.3
The second
PCP
result
............... 238
7.3
The final proof
....................... 239
7.3.1
Normal form verifiers
............... 241
7.3.2
The composition lemma
.............. 245
7.4
Exercises
.......................... 248
7.5
Bibliographical notes
.................... 249
8
Approximation Preserving Reductions
253
8.1
The World of NPO Problems
................ 254
8.2
AP-reducibility
....................... 256
8.2.1
Complete problems
................. 261
8.3
NPO-completeness
..................... 261
8.3.1
Other NPO-complete problems
........... 265
8.3.2
Completeness in exp-APX
............. 265
8.4
APX-completeness
..................... 266
8.4.1
Other APX-complete problems
........... 270
8.5
Exercises
.......................... 281
8.6
Bibliographical notes
.................... 283
9
Probabilistic analysis of approximation algorithms
287
9.1
Introduction
......................... 288
9.1.1
Goals of probabilistic analysis
........... 289
9.2
Techniques for the probabilistic analysis of algorithms
. . 291
9.2.1
Conditioning in the analysis of algorithms
..... 291
9.2.2
The first and the second moment methods
..... 293
9.2.3
Convergence of random variables
......... 294
9.3
Probabilistic analysis and multiprocessor scheduling
. . . 296
9.4
Probabilistic analysis and bin packing
........... 298
9.5
Probabilistic analysis and maximum clique
........ 302
9.6
Probabilistic analysis and graph coloring
.......... 311
9.7
Probabilistic analysis and Euclidean TSP
.......... 312
9.8
Exercises
.......................... 316
9.9
Bibliographical notes
.................... 318
10
Heuristic methods
321
10.1
Types of heuristics
..................... 322
10.2
Construction heuristics
................... 325
----- 10.3
Local search heuristics
................... 329
Table
of contents
10.3.1
Fixed-depth local search heuristics
......... 330
10.3.2
Variable-depth local search heuristics
....... 336
10.4
Heuristics based on local search
.............. 341
10.4.1
Simulated annealing
................ 341
10.4.2
Genetic algorithms
................. 344
10.4.3
Tabu search
..................... 347
10.5
Exercises
.......................... 349
10.6
Bibliographical notes
.................... 350
A Mathematical preliminaries
353
A.I Sets
............................. 353
A.
1.1
Sequences, tuples and matrices
........... 354
A.2 Functions and relations
................... 355
A.3 Graphs
............................ 356
A.4 Strings and languages
.................... 357
A.5 Boolean logic
........................ 357
A.6 Probability
.......................... 358
A.6.1 Random variables
.................. 359
A.7 Linear programming
.................... 361
A.8 Two famous formulas
.................... 365
В
A List of
NP
Optimization Problems
367
Bibliography *^1
Index 515
XI
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV017119223 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
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| ctrlnum | (OCoLC)249492438 (DE-599)BVBBV017119223 |
| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2., corr. print. |
| format | Book |
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| id | DE-604.BV017119223 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:43:23Z |
| institution | BVB |
| isbn | 3540654313 9783540654315 |
| language | English |
| lccn | 99040936 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010321378 |
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| physical | XIX, 524 S. graph. Darst. 1 CD-ROM (12 cm) |
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| publisher | Springer |
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| spellingShingle | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables Kombinatorische Optimierung - Komplexitätstheorie - NP-vollständiges Problem - Approximationsalgorithmus Combinatorial optimization Computational complexity Computer algorithms Komplexitätstheorie (DE-588)4120591-1 gnd NP-vollständiges Problem (DE-588)4138229-8 gnd Approximationsalgorithmus (DE-588)4500954-5 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4138229-8 (DE-588)4500954-5 (DE-588)4031826-6 |
| title | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables |
| title_auth | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables |
| title_exact_search | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables |
| title_full | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables G. Ausiello ... |
| title_fullStr | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables G. Ausiello ... |
| title_full_unstemmed | Complexity and approximation combinatorial optimization problems and their approximability properties ; with 4 tables G. Ausiello ... |
| title_short | Complexity and approximation |
| title_sort | complexity and approximation combinatorial optimization problems and their approximability properties with 4 tables |
| title_sub | combinatorial optimization problems and their approximability properties ; with 4 tables |
| topic | Kombinatorische Optimierung - Komplexitätstheorie - NP-vollständiges Problem - Approximationsalgorithmus Combinatorial optimization Computational complexity Computer algorithms Komplexitätstheorie (DE-588)4120591-1 gnd NP-vollständiges Problem (DE-588)4138229-8 gnd Approximationsalgorithmus (DE-588)4500954-5 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd |
| topic_facet | Kombinatorische Optimierung - Komplexitätstheorie - NP-vollständiges Problem - Approximationsalgorithmus Combinatorial optimization Computational complexity Computer algorithms Komplexitätstheorie NP-vollständiges Problem Approximationsalgorithmus Kombinatorische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010321378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ausiellogiorgio complexityandapproximationcombinatorialoptimizationproblemsandtheirapproximabilitypropertieswith4tables |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 890 A932 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |