Complexity theory: exploring the limits of efficient algorithms
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013160413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XI, 308 S. graph. Darst. |
| ISBN: | 3540210458 9783540210450 |
Staff View
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 DAT 517f 2005 A 9060 0104 DAT 517f 2005 A 9060 |
|---|---|
| DE-BY-TUM_katkey | 1525527 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071007162 040020059372 |
| _version_ | 1821932679789019136 |
| adam_text | Contents
1
Introduction
............................................... 1
1.1
What Is Complexity Theory?
............................. 1
1.2
Didactic Background
..................................... 5
1.3
Overview
............................................... 6
1.4
Additional Literature
.................................... 10
2
Algorithmic Problems
&
Their Complexity
................ 11
2.1
What Are Algorithmic Problems?
......................... 11
2.2
Some Important Algorithmic Problems
..................... 13
2.3
Measuring Computation Time
............................ 18
2.4
The Complexity of Algorithmic Problems
................... 22
3
Fundamental Complexity Classes
.......................... 25
3.1
The Special Role of Polynomial Computation Time
.......... 25
3.2
Randomized Algorithms
.................................. 27
3.3
The Fundamental Complexity Classes for Algorithmic Problems
30
3.4
The Fundamental Complexity Classes for Decision Problems
. . 35
3.5
Nondeterminism as a Special Case of Randomization
......... 39
4
Reductions
-
Algorithmic Relationships Between Problems
43
4.1
When Are Two Problems Algorithmically Similar?
........... 43
4.2
Reductions Between Various Variants of a Problem
.......... 46
4.3
Reductions Between Related Problems
..................... 49
4.4
Reductions Between Unrelated Problems
................... 53
4.5
The Special Role of Polynomial Reductions
................. 60
5
The Theory of NP-Completeness
.......................... 63
5.1
Fundamental Considerations
.............................. 63
5.2
Problems in NP
......................................... 67
5.3
Alternative Characterizations of NP
....................... 69
5.4
Cook s Theorem
......................................... 70
6
NP-complete and NP-equivalent Problems
................. 77
6.1 Fundamental
Considerations
.............................. 77
6.2
Traveling Salesperson Problems
........................... 77
6.3
Knapsack Problems
...................................... 78
6.4
Partitioning and Scheduling Problems
...................... 80
6.5
Clique Problems
......................................... 81
6.6
Team Building Problems
................................. 83
6.7
Championship Problems
.................................. 85
7
The Complexity Analysis of Problems
..................... 89
7.1
The Dividing Line Between Easy and Hard
................. 89
7.2
Pseudo-polynomial Algorithms and Strong NP-completeness
.. 93
7.3
An Overview of the NP-completeness Proofs Considered
...... 96
8
The Complexity of Approximation Problems
-
Classical
Results
.................................................... 99
8.1
Complexity Classes
...................................... 99
8.2
Approximation Algorithms
...............................103
8.3
The Gap Technique
......................................106
8.4
Approximation-Preserving Reductions
......................109
8.5
Complete Approximation Problems
........................112
9
The Complexity of Black Box Problems
...................115
9.1
Black Box Optimization
..................................115
9.2
Yao s Minimax Principle
.................................118
9.3
Lower Bounds for Black Box Complexity
...................120
10
Additional Complexity Classes
.............................127
10.1
Fundamental Considerations
..............................127
10.2
Complexity Classes Within NP and co-NP
..................128
10.3
Oracle Classes
..........................................130
10.4
The Polynomial Hierarchy
.................................132
10.5
BPP, NP, and the Polynomial Hierarchy
....................138
11
Interactive Proofs
..................
í
......................145
11.1
Fundamental Considerations
..............................145
11.2
Interactive Proof Systems
................................147
11.3
Regarding the Complexity of Graph Isomorphism Problems
. . . 148
11.4
Zero-Knowledge Proofs
...................................155
12
The
PCP
Theorem and the Complexity o;f Approximation
Problems
...................................................161
12.1
Randomized Verification of Proofs
....... ..................161
12.2
The
PCP
Theorem
....................;.................164
12.3
The
PCP
Theorem and Inapproximability Results
...........173
12.4
The
PCP
Theorem and APX-Completeness1,
.................177
13
Further Topics From Classical Complexity Theory
.........185
13.1
Overview
...............................................185
13.2
Space-Bounded Complexity Classes
........................186
13.3
PSPACE-complete Problems
..............................188
13.4
Nondeterminism and Determinism in the Context of Bounded
Space
..................................................191
13.5
Nondeterminism and Complementation with Precise Space
Bounds
................................................193
13.6
Complexity Classes Within
Ρ
.............................195
13.7
The Complexity of Counting Problems
.....................198
14
The Complexity of Non-uniform Problems
.................201
14.1
Fundamental Considerations
..............................201
14.2
The Simulation of Turing Machines By Circuits
.............204
14.3
The Simulation of Circuits by Non-uniform Turing Machines
. . 206
14.4
Branching Programs and Space Bounds
....................209
14.5
Polynomial Circuits for Problems in BPP
...................211
14.6
Complexity Classes for Computation with Help
.............212
14.7
Are There Polynomial Circuits for all Problems in NP?
.......214
15
Communication Complexity
...............................219
15.1
The Communication Game
...............................219
15.2
Lower Bounds for Communication Complexity
..............223
15.3
Nondeterministic Communication Protocols
.................233
15.4
Randomized Communication Protocols
.....................238
15.5
Communication Complexity and VLSI Circuits
..............246
15.6
Communication Complexity and Computation Time
.........247
16
The Complexity of Boolean Functions
.....................251
16.1
Fundamental Considerations
..............................251
16.2
Circuit Size
.............................................252
16.3
Circuit Depth
...........................................254
16.4
The Size of Depth-Bounded Circuits
.......................259
16.5
The Size of Depth-Bounded Threshold Circuits
..............264
16.6
The Size of Branching Programs
...........................26?
16.7
Reduction Notions
................................,......271
Final Comments
...............................................
2Y7
A Appendix
..................................................279
A.I Orders of Magnitude and
О
-Notation......................
279
A.
2
Results from Probability Theory
..........................283
References
.....................................................295
Index
..........................................................301
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.1 |
| dewey-search | 518.1 |
| dewey-sort | 3518.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV019835418 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:06:54Z |
| institution | BVB |
| isbn | 3540210458 9783540210450 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013160413 |
| oclc_num | 249520145 |
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| physical | XI, 308 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Wegener, Ingo 1950-2008 Complexity theory exploring the limits of efficient algorithms Komplexitätstheorie - Lehrbuch Algorithms Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4123623-3 |
| title | Complexity theory exploring the limits of efficient algorithms |
| title_alt | Komplexitätstheorie |
| title_auth | Complexity theory exploring the limits of efficient algorithms |
| title_exact_search | Complexity theory exploring the limits of efficient algorithms |
| title_full | Complexity theory exploring the limits of efficient algorithms Ingo Wegener |
| title_fullStr | Complexity theory exploring the limits of efficient algorithms Ingo Wegener |
| title_full_unstemmed | Complexity theory exploring the limits of efficient algorithms Ingo Wegener |
| title_short | Complexity theory |
| title_sort | complexity theory exploring the limits of efficient algorithms |
| title_sub | exploring the limits of efficient algorithms |
| topic | Komplexitätstheorie - Lehrbuch Algorithms Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Komplexitätstheorie - Lehrbuch Algorithms Komplexitätstheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013160413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wegeneringo komplexitatstheorie AT wegeneringo complexitytheoryexploringthelimitsofefficientalgorithms |
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| Call Number: |
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