Parameterized complexity theory:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Series: | Texts in theoretical computer science
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [463] - 475 |
| Physical Description: | XIII, 493 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540299523 3540299521 |
Staff View
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Record in the Search Index
| _version_ | 1814812060678094848 |
|---|---|
| adam_text |
J. FLUM YY M. GROHE
PARAMETERIZED
COMPLEXITY THEORY
WITH 51 FIGURES
4Y SPRINGER
CONTENTS
1 FIXED-PARAMETE
R TRACTABILIT
Y
1
1.1 INTRODUCTION 1
1.2 PARAMETERIZED PROBLEMS AND FIXED-PARAMETER TRACTABILITY .
. 3
1.3 HITTING SETS AND TH
E METHOD OF BOUNDED SEARCH TREES 10
1.4 APPROXIMABILITY AND FIXED-PARAMETER TRACTABILITY 19
1.5 MODEL-CHECKING PROBLEMS 24
1.6 ALTERNATIVE CHARACTERIZATIONS OF FIXED-PARAMETER TRACTABILITY. . 26
2 REDUCTION
S AN
D PARAMETERIZE
D INTRACTABILIT
Y
33
2.1 FIXED-PARAMETER TRACTABLE REDUCTIONS 33
2.2 THE CLASS PARA-NP 37
2.3 THE CLASS XP 41
3
TH
E CLAS
S
W[P
] 45
3.1 DEFINITION AND BASIC RESULTS 45
3.2 W[P]-COMPLETE PROBLEMS 49
3.3 IS FP
T 7^ W[P]? 57
4 LOGIC AN
D COMPLEXIT
Y
65
4.1 PROPOSITIONAL LOGIC 66
4.2 FIRST-ORDER AND SECOND-ORDER LOGIC 72
4.3 THE COMPLEXITY OF FIRST-ORDER AND SECOND-ORDER LOGIC 81
4.4 OPTIMIZATION PROBLEMS AND LIMITED NONDETERMINISM 88
5 TW
O FUNDAMENTA
L HIERARCHIE
S
95
5.1
THE W-HIERARCHY 95
5.2 THE A-HIERARCHY 98
6 TH
E FIRS
T LEVEL OF TH
E HIERARCHIE
S
105
6.1
A[L]-COMPLETE PROBLEMS 106
6.2 A[L] AND MACHINES 114
XII CONTENTS
6.3 A[L] AND PROPOSITIONAL LOGIC 123
6.4 A[L] = W[L] 128
7 TH
E W-HIERARCHY
133
7.1 THE W-HIERARCHY AND PROPOSITIONAL LOGIC 133
7.2 W[2]-COMPLETE PROBLEMS 143
7.3 THE W-HIERARCHY AND CIRCUITS 147
7.4 THE W-HIERARCHY AND FIRST-ORDER LOGIC 148
7.5 W[2] AND TURING MACHINES 153
7.6 THE MONOTONE AND ANTIMONOTONE COLLAPSE 156
7.7 THE CLASS W[SAT] 162
8
TH
E A-HIERARCHY
165
8.1 THE A-HIERARCHY AND MACHINES 165
8.2 ^-NORMALIZATIO
N 171
8.3 THE A-HIERARCHY AND PROPOSITIONAL LOGIC 174
8.4 COMPLETE PROBLEMS FOR A[2] AND CO-A[L] 180
8.5 THE A-HIERARCHY AND FAGIN DEFINABILITY 186
8.6 THE CLASSES AW[*] AND AW[P] 188
8.7 THE A-MATRIX 195
8.8 BACK TO THE W-HIERARCHY 197
9 KERNELIZATIO
N AND LINEAR PROGRAMMIN
G TECHNIQUES
207
9.1 POLYNOMIAL KERNELIZATIONS 208
9.2 CROWN RULE REDUCTIONS 212
9.3 KERNELIZATION THROUGH LINEAR PROGRAMMING 218
9.4 INTEGER LINEAR PROGRAMMING 222
10 TH
E AUTOMATA-THEORETI
C APPROACH
233
10.1 MODEL-CHECKING ON STRINGS 234
10.2 MODEL-CHECKING ON TREES 245
10.3 LOWER BOUNDS 249
11 TREE WIDT
H
261
11.1 TREE DECOMPOSITIONS OF GRAPHS 262
11.2 COMPUTING TREE DECOMPOSITIONS 266
11.3 TREE DECOMPOSITIONS OF ARBITRARY STRUCTURES 275
11.4 ALGORITHMS ON STRUCTURES OF BOUNDED TREE WIDTH 278
11.5 APPLICATIONS OF COURCELLE'S THEOREM 286
11.6 TREE WIDTH REDUCTION 292
11.7 GRAPH MINORS 295
CONTENTS XIII
12 PLANARIT
Y AND BOUNDE
D LOCAL TREE WIDT
H
301
12.1 ALGORITHMS ON PLANAR GRAPHS 302
12.2 LOCAL TREE WIDTH 313
12.3 MINOR CLOSED CLASSES 320
12.4 IMPROVED PLANAR GRAPH ALGORITHMS 321
13
HOMOMORPHISM
S AND EMBEDDING
S
327
13.1 TRACTABLE RESTRICTIONS OF THE HOMOMORPHISM PROBLEM 327
13.2 THE COMPLEXITY OF THE HOMOMORPHISM PROBLEM 336
13.3 COLOR CODING AND THE EMBEDDING PROBLEM 342
14 PARAMETERIZE
D COUNTIN
G PROBLEM
S
357
14.1 FIXED-PARAMETER TRACTABLE COUNTING PROBLEMS 357
14.2 INTRACTABLE PARAMETERIZED COUNTING PROBLEMS 361
14.3 #W[1]-COMPLETE PROBLEMS 367
14.4 THE COMPLEXITY OF COUNTING PATHS AND CYCLES 372
14.5 APPROXIMATE COUNTING 384
15 BOUNDE
D FIXED-PARAMETE
R TRACTABILITY
389
15.1 THE BOUNDED FRAMEWORK 390
15.2 THE CLASS EW[P] AND LIMITED NONDETERMINISM 394
15.3 THE EW-HIERARCHY 397
15.4 COMPLETE PROBLEMS 402
15.5 THE EW-HIERARCHY AND THE LOG-HIERARCHY 407
15.6 HIGHER LEVELS OF INTRACTABILITY 412
16 SUBEXPONENTIA
L FIXED-PARAMETE
R TRACTABILITY
417
16.1 SIZE-MEASURES AND REDUCTIONS 418
16.2 A HIERARCHY WITHIN EP
T 422
16.3 THE SPARSIFICATION LEMMA 426
16.4 S[1]-COMPLETENESS 435
16.5 THE MINIATURIZATION ISOMORPHISM 438
16.6 THE M-HIERARCHY 443
A APPENDIX
: BACKGROUND FROM COMPLEXIT
Y THEOR
Y
453
A.I MACHINE MODELS 454
A.2 COMPLEXITY CLASSES 460
REFERENCES
463
NOTATIO
N
477
INDE
X 481 |
| adam_txt |
J. FLUM YY M. GROHE
PARAMETERIZED
COMPLEXITY THEORY
WITH 51 FIGURES
4Y SPRINGER
CONTENTS
1 FIXED-PARAMETE
R TRACTABILIT
Y
1
1.1 INTRODUCTION 1
1.2 PARAMETERIZED PROBLEMS AND FIXED-PARAMETER TRACTABILITY .
. 3
1.3 HITTING SETS AND TH
E METHOD OF BOUNDED SEARCH TREES 10
1.4 APPROXIMABILITY AND FIXED-PARAMETER TRACTABILITY 19
1.5 MODEL-CHECKING PROBLEMS 24
1.6 ALTERNATIVE CHARACTERIZATIONS OF FIXED-PARAMETER TRACTABILITY. . 26
2 REDUCTION
S AN
D PARAMETERIZE
D INTRACTABILIT
Y
33
2.1 FIXED-PARAMETER TRACTABLE REDUCTIONS 33
2.2 THE CLASS PARA-NP 37
2.3 THE CLASS XP 41
3
TH
E CLAS
S
W[P
] 45
3.1 DEFINITION AND BASIC RESULTS 45
3.2 W[P]-COMPLETE PROBLEMS 49
3.3 IS FP
T 7^ W[P]? 57
4 LOGIC AN
D COMPLEXIT
Y
65
4.1 PROPOSITIONAL LOGIC 66
4.2 FIRST-ORDER AND SECOND-ORDER LOGIC 72
4.3 THE COMPLEXITY OF FIRST-ORDER AND SECOND-ORDER LOGIC 81
4.4 OPTIMIZATION PROBLEMS AND LIMITED NONDETERMINISM 88
5 TW
O FUNDAMENTA
L HIERARCHIE
S
95
5.1
THE W-HIERARCHY 95
5.2 THE A-HIERARCHY 98
6 TH
E FIRS
T LEVEL OF TH
E HIERARCHIE
S
105
6.1
A[L]-COMPLETE PROBLEMS 106
6.2 A[L] AND MACHINES 114
XII CONTENTS
6.3 A[L] AND PROPOSITIONAL LOGIC 123
6.4 A[L] = W[L] 128
7 TH
E W-HIERARCHY
133
7.1 THE W-HIERARCHY AND PROPOSITIONAL LOGIC 133
7.2 W[2]-COMPLETE PROBLEMS 143
7.3 THE W-HIERARCHY AND CIRCUITS 147
7.4 THE W-HIERARCHY AND FIRST-ORDER LOGIC 148
7.5 W[2] AND TURING MACHINES 153
7.6 THE MONOTONE AND ANTIMONOTONE COLLAPSE 156
7.7 THE CLASS W[SAT] 162
8
TH
E A-HIERARCHY
165
8.1 THE A-HIERARCHY AND MACHINES 165
8.2 ^-NORMALIZATIO
N 171
8.3 THE A-HIERARCHY AND PROPOSITIONAL LOGIC 174
8.4 COMPLETE PROBLEMS FOR A[2] AND CO-A[L] 180
8.5 THE A-HIERARCHY AND FAGIN DEFINABILITY 186
8.6 THE CLASSES AW[*] AND AW[P] 188
8.7 THE A-MATRIX 195
8.8 BACK TO THE W-HIERARCHY 197
9 KERNELIZATIO
N AND LINEAR PROGRAMMIN
G TECHNIQUES
207
9.1 POLYNOMIAL KERNELIZATIONS 208
9.2 CROWN RULE REDUCTIONS 212
9.3 KERNELIZATION THROUGH LINEAR PROGRAMMING 218
9.4 INTEGER LINEAR PROGRAMMING 222
10 TH
E AUTOMATA-THEORETI
C APPROACH
233
10.1 MODEL-CHECKING ON STRINGS 234
10.2 MODEL-CHECKING ON TREES 245
10.3 LOWER BOUNDS 249
11 TREE WIDT
H
261
11.1 TREE DECOMPOSITIONS OF GRAPHS 262
11.2 COMPUTING TREE DECOMPOSITIONS 266
11.3 TREE DECOMPOSITIONS OF ARBITRARY STRUCTURES 275
11.4 ALGORITHMS ON STRUCTURES OF BOUNDED TREE WIDTH 278
11.5 APPLICATIONS OF COURCELLE'S THEOREM 286
11.6 TREE WIDTH REDUCTION 292
11.7 GRAPH MINORS 295
CONTENTS XIII
12 PLANARIT
Y AND BOUNDE
D LOCAL TREE WIDT
H
301
12.1 ALGORITHMS ON PLANAR GRAPHS 302
12.2 LOCAL TREE WIDTH 313
12.3 MINOR CLOSED CLASSES 320
12.4 IMPROVED PLANAR GRAPH ALGORITHMS 321
13
HOMOMORPHISM
S AND EMBEDDING
S
327
13.1 TRACTABLE RESTRICTIONS OF THE HOMOMORPHISM PROBLEM 327
13.2 THE COMPLEXITY OF THE HOMOMORPHISM PROBLEM 336
13.3 COLOR CODING AND THE EMBEDDING PROBLEM 342
14 PARAMETERIZE
D COUNTIN
G PROBLEM
S
357
14.1 FIXED-PARAMETER TRACTABLE COUNTING PROBLEMS 357
14.2 INTRACTABLE PARAMETERIZED COUNTING PROBLEMS 361
14.3 #W[1]-COMPLETE PROBLEMS 367
14.4 THE COMPLEXITY OF COUNTING PATHS AND CYCLES 372
14.5 APPROXIMATE COUNTING 384
15 BOUNDE
D FIXED-PARAMETE
R TRACTABILITY
389
15.1 THE BOUNDED FRAMEWORK 390
15.2 THE CLASS EW[P] AND LIMITED NONDETERMINISM 394
15.3 THE EW-HIERARCHY 397
15.4 COMPLETE PROBLEMS 402
15.5 THE EW-HIERARCHY AND THE LOG-HIERARCHY 407
15.6 HIGHER LEVELS OF INTRACTABILITY 412
16 SUBEXPONENTIA
L FIXED-PARAMETE
R TRACTABILITY
417
16.1 SIZE-MEASURES AND REDUCTIONS 418
16.2 A HIERARCHY WITHIN EP
T 422
16.3 THE SPARSIFICATION LEMMA 426
16.4 S[1]-COMPLETENESS 435
16.5 THE MINIATURIZATION ISOMORPHISM 438
16.6 THE M-HIERARCHY 443
A APPENDIX
: BACKGROUND FROM COMPLEXIT
Y THEOR
Y
453
A.I MACHINE MODELS 454
A.2 COMPLEXITY CLASSES 460
REFERENCES
463
NOTATIO
N
477
INDE
X 481 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T14:40:00Z |
| indexdate | 2024-11-04T17:00:51Z |
| institution | BVB |
| isbn | 9783540299523 3540299521 |
| language | English |
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| physical | XIII, 493 Seiten Illustrationen, Diagramme |
| publishDate | 2006 |
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| publisher | Springer |
| record_format | marc |
| series2 | Texts in theoretical computer science |
| spelling | Flum, Jörg 1944- Verfasser (DE-588)121343391 aut Parameterized complexity theory J. Flum ; M. Grohe Berlin [u.a.] Springer 2006 XIII, 493 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Literaturverz. S. [463] - 475 Algorithms Computational complexity Parametrisierte Komplexität (DE-588)4818897-9 gnd rswk-swf Parametrisierte Komplexität (DE-588)4818897-9 s DE-604 Grohe, Martin 1967- Verfasser (DE-588)1019542179 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2768760&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791571&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Flum, Jörg 1944- Grohe, Martin 1967- Parameterized complexity theory Algorithms Computational complexity Parametrisierte Komplexität (DE-588)4818897-9 gnd |
| subject_GND | (DE-588)4818897-9 |
| title | Parameterized complexity theory |
| title_auth | Parameterized complexity theory |
| title_exact_search | Parameterized complexity theory |
| title_exact_search_txtP | Parameterized complexity theory |
| title_full | Parameterized complexity theory J. Flum ; M. Grohe |
| title_fullStr | Parameterized complexity theory J. Flum ; M. Grohe |
| title_full_unstemmed | Parameterized complexity theory J. Flum ; M. Grohe |
| title_short | Parameterized complexity theory |
| title_sort | parameterized complexity theory |
| topic | Algorithms Computational complexity Parametrisierte Komplexität (DE-588)4818897-9 gnd |
| topic_facet | Algorithms Computational complexity Parametrisierte Komplexität |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2768760&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791571&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT flumjorg parameterizedcomplexitytheory AT grohemartin parameterizedcomplexitytheory |