Invitation to fixed-parameter algorithms:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford <<[u.a.]>>
Oxford Univ. Press
2008
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
31 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018883050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | XI, 300 S. graph. Darst. |
| ISBN: | 9780198566076 |
Internformat
MARC
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| 245 | 1 | 0 | |a Invitation to fixed-parameter algorithms |c Rolf Niedermeier |
| 250 | |a Reprint. | ||
| 264 | 1 | |a Oxford <<[u.a.]>> |b Oxford Univ. Press |c 2008 | |
| 300 | |a XI, 300 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 31 | |
| 500 | |a Includes bibliographical references and index | ||
| 502 | |a Teilw. zugl.: Tübingen, Univ., Habil.-Schr., 2002 | ||
| 650 | 7 | |a Algorithms |2 blmsh | |
| 650 | 4 | |a Algorithmus - Parameterschätzung - Kombinatorische Analysis | |
| 650 | 7 | |a Combinatorial analysis |2 blmsh | |
| 650 | 7 | |a Parameter estimation |2 blmsh | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 4 | |a Parameter estimation | |
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Datensatz im Suchindex
| _version_ | 1819290922623434752 |
|---|---|
| adam_text | CONTENTS
I FOUNDATIONS
1
Introduction to Fixed-Parameter Algorithms
3
1.1
The satisfiability problem
4
1.2
An example from railway optimization
7
1.3
A communication problem in tree networks
10
1.4
Summary
12
1.5
Exercises
13
1.6
Bibliographical remarks
14
2
Preliminaries and Agreements
17
2.1
Basic sets and problems
17
2.2
Model of computation and running times
17
2.3
Strings and graphs
18
2.4
Complexity and approximation
20
2.5
Bibliographical remarks
21
3
Parameterized Complexity Theory
—
A Primer
22
3.1
Basic theory
22
3.2
Interpreting fixed-parameter tractability
27
3.3
Exercises
29
3.4
Bibliographical remarks
29
4
Vertex Cover
—
An Illustrative Example
31
4.1
Parameterizing
32
4.2
Specializing
33
4.3
Generalizing
34
4.4
Counting or enumerating
34
4.5
Lower bounds
35
4.6
Implementing and applying
35
4.7
Using vertex cover structure for other problems
36
4.8
Exercises
38
4.9
Bibliographical remarks
38
5
The Art of Problem Parameterization
41
5.1
Parameter really small?
41
5.2
Guaranteed parameter value?
42
5.3
More than one obvious parameterization?
43
5.4
Close to trivial problem instances?
45
5.5
Exercises
47
5.6
Bibliographical remarks
47
vu
viii CONTENTS
6
Summary and Concluding Remarks
49
II ALGORITHMIC METHODS
7
Data Reduction and Problem Kernels
53
7.1
Basic definitions and facts
55
7.2
Maximum Satisfiability
58
7.3
Cluster Editing
60
7.4
Vertex Cover
64
7.4.1
Kernelization based on matching
64
7.4.2
Kernelization based on linear programming
68
7.4.3
Kernelization based on crown structures
69
7.4.4
Comparison and discussion
72
7.5
3-Hitting Set
72
7.6
Dominating Set in Planar Graphs
74
7.6.1
The neighborhood of a single vertex
74
7.6.2
The neighborhood of a pair of vertices
77
7.6.3
Reduced graphs and the problem kernel
79
7.7
On lower bounds for problem kernels
80
7.8
Summary and concluding remarks
82
7.9
Exercises
83
7.10
Bibliographical remarks
85
8
Depth-Bounded Search Trees
88
8.1
Basic definitions and facts
91
8.2
Cluster Editing
93
8.3
Vertex Cover
98
8.4
Hitting Set
101
8.5
Closest String
103
8.6
Dominating Set in Planar Graphs
107
8.6.1
Data reduction rules
108
8.6.2
Main result and some remarks
109
8.7
Interleaving search trees and kernelization
110
8.7.1
Basic methodology 111
8.7.2
Interleaving is necessary
113
8.8
Automated search tree generation and analysis
114
8.9
Summary and concluding remarks
119
8.10
Exercises
120
8.11
Bibliographical remarks
121
9
Dynamic Programming
124
9.1
Basic definitions and facts
125
9.2
Knapsack
126
9.3 Steiner
Problem in Graphs
128
9.4
Multicommodity Demand Flow in Trees
131
CONTENTS ix
9.5
Tree-structured variants of Set Cover
136
9.5.1
Basic definitions and facts
136
9.5.2
Algorithm for Path-like Weighted Set Cover
139
9.5.3
Algorithm for Tree-like Weighted Set Cover
140
9.6
Shrinking search trees
145
9.7
Summary and concluding remarks
146
9.8
Exercises
147
9.9
Bibliographical remarks
148
10
Tree Decompositions of Graphs
150
10.1
Basic definitions and facts
151
10.2
On the construction of tree decompositions
153
10.3
Planar graphs
155
10.4
Dynamic programming for Vertex Cover
160
10.5
Dynamic programming for Dominating Set
164
10.6
Monadic second-order logic (MSO)
169
10.7
Related graph width parameters
172
10.8
Summary and concluding remarks
174
10.9
Exercises
175
lO.lOBibliographical remarks
176
11
Further Advanced Techniques
177
11.1
Color-coding
178
11.2
Integer linear programming
181
11.3
Iterative compression
184
11.3.1
Vertex Cover
185
11.3.2
Feedback Vertex Set
187
11.4
Greedy localization
190
11.4.1
Set Splitting
191
11.4.2
Set Packing
193
11.5
Graph minor theory
195
11.6
Summary and concluding remarks
197
11.7
Exercises
198
11.8
Bibliographical remarks
199
12
Summary and Concluding Remarks
201
III SOME THEORY, SOME CASE STUDIES
13
Parameterized Complexity Theory
205
13.1
Basic definitions and concepts
206
13.1.1
Parameterized reducibility
207
13.1.2
Parameterized complexity classes
209
13.2
The complexity class W[l]
212
13.3
Concrete parameterized reductions
216
13.3.1
ИфЈ
-hardness
proofs
218
x
CONTENTS
13.3.2
Further reductions and W^J-hardness
226
13.4
Some recent developments
230
13.4.1
Lower bounds and the complexity class M[l]
230
13.4.2
Lower bounds and linear FPT reductions
232
13.4.3
Machine models, limited nondeterminism, and
bounded FPT
233
13.5
Summary and concluding remarks
234
13.6
Exercises
235
13.7
Bibliographical remarks
235
14
Connections to Approximation Algorithms
237
14.1
Approximation helping parameterization
238
14.2
Parameterization helping approximation
239
14.3
Further (non-)relations
241
14.4
Discussion and concluding remarks
241
14.5
Bibliographical remarks
242
15
Selected Case Studies
243
15.1
Planar and more general graphs
243
15.1.1
Planar graphs
243
15.1.2
More general graphs
245
15.2
Graph modification problems
245
15.2.1
Graph modification and hereditary properties
246
15.2.2
Feedback Vertex Set revisited
247
15.2.3
Graph Bipartization
248
15.2.4
Minimum Fill-in
249
15.2.5
Closest 3-Leaf Power
250
15.3
Miscellaneous graph problems
251
15.3.1
Capacitated Vertex Cover
251
15.3.2
Constraint Bipartite Vertex Cover
253
15.3.3
Graph Coloring
255
15.3.4
Crossing Number
256
15.3.5
Power Dominating Set
257
15.4
Computational biology problems
258
15.4.1
Minimum Quartet Inconsistency
259
15.4.2
Compatibility of Unrooted Phvlogenetic Trees
261
15.4.3
Longest Arc-Preserving Common Subsequences
262
15.4.4
Incomplete Perfect Path Phylogeny Haplotyp-
ing
264
15.5
Logic and related problems
266
15.5.1
Satisfiability
266
15.5.2
Maximum Satisfiability
268
15.5.3
Constraint satisfaction problems
269
15.5.4
Database queries
270
15.6
Miscellaneous problems
271
CONTENTS xi
15.6.1
Two-dimensional Euclidean TSP
272
15.6.2
Multidimensional matching
273
15.6.3
Matrix Domination
273
15.6.4
Vapnik-Chervonenkis Dimension
274
15.7
Summary and concluding remarks
275
16 Zukunftsmusik 277
References
279
Index
294
|
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| dewey-search | 518.1 |
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| discipline | Informatik Mathematik |
| edition | Reprint. |
| format | Thesis Book |
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| id | DE-604.BV035990330 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:04:34Z |
| institution | BVB |
| isbn | 9780198566076 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018883050 |
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| physical | XI, 300 S. graph. Darst. |
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| series2 | Oxford lecture series in mathematics and its applications |
| spellingShingle | Niedermeier, Rolf 19XX- Invitation to fixed-parameter algorithms Oxford lecture series in mathematics and its applications Algorithms blmsh Algorithmus - Parameterschätzung - Kombinatorische Analysis Combinatorial analysis blmsh Parameter estimation blmsh Algorithms Combinatorial analysis Parameter estimation Algorithmus (DE-588)4001183-5 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4164746-4 (DE-588)4044614-1 (DE-588)4113937-9 |
| title | Invitation to fixed-parameter algorithms |
| title_auth | Invitation to fixed-parameter algorithms |
| title_exact_search | Invitation to fixed-parameter algorithms |
| title_full | Invitation to fixed-parameter algorithms Rolf Niedermeier |
| title_fullStr | Invitation to fixed-parameter algorithms Rolf Niedermeier |
| title_full_unstemmed | Invitation to fixed-parameter algorithms Rolf Niedermeier |
| title_short | Invitation to fixed-parameter algorithms |
| title_sort | invitation to fixed parameter algorithms |
| topic | Algorithms blmsh Algorithmus - Parameterschätzung - Kombinatorische Analysis Combinatorial analysis blmsh Parameter estimation blmsh Algorithms Combinatorial analysis Parameter estimation Algorithmus (DE-588)4001183-5 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Algorithms Algorithmus - Parameterschätzung - Kombinatorische Analysis Combinatorial analysis Parameter estimation Algorithmus Kombinatorische Analysis Parameterschätzung Hochschulschrift |
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