Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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Univ.-Verl. der TU Berlin
2014
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| Schriftenreihe: | Foundations of computing
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| 100 | 1 | |a Bevern, René van |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations |c René van Bevern |
| 246 | 1 | |a Fixed-parameter linear-time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations | |
| 264 | 1 | |a Berlin |b Univ.-Verl. der TU Berlin |c 2014 | |
| 300 | |a XIX, 205 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Foundations of computing |v 1 | |
| 502 | |a Zugl.: Berlin, Techn. Univ., Diss., 2014 | ||
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| 650 | 0 | 7 | |a Effizienter Algorithmus |0 (DE-588)4125422-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hypergraph |0 (DE-588)4161063-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Graph |0 (DE-588)4021842-9 |D s |
| 689 | 0 | 2 | |a Hypergraph |0 (DE-588)4161063-5 |D s |
| 689 | 0 | 3 | |a Berechnungskomplexität |0 (DE-588)4134751-1 |D s |
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| 912 | |a ebook | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027774432 | ||
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001/2015 A 731 |
|---|---|
| DE-BY-TUM_katkey | 2055313 |
| DE-BY-TUM_media_number | 040007903968 |
| _version_ | 1816714036584120320 |
| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 FIXED-PARAMETER LINEAR-TIME ALGORITHMS 3
1.2 LINEAR-TIME KERNELIZATION 4
1.3 OVERVIEW 5
2 PRELIMINARIES 7
2.1 SETS, RELATIONS, AND FUNCTIONS 7
2.2 GRAPH THEORY 10
2.2.1 GRAPHS AND HYPERGRAPHS 10
2.2.2 RELATIONS AND OPERATIONS ON GRAPHS 12
2.2.3 STRUCTURES, TOPOLOGY, AND PARAMETERS 14
2.2.4 GRAPH CLASSES AND SPECIAL GRAPHS 16
2.3 COMPUTATIONAL COMPLEXITY 17
2.3.1 WHAT IS TIME? 18
2.3.2 OPTIMIZATION PROBLEMS VERSUS DECISION PROBLEMS 19
2.3.3 P VERSUS NP 20
2.3.4 NP-HARDNESS AND COMPLETENESS 21
2.4 PARAMETERIZED COMPLEXITY 22
2.4.1 FIXED-PARAMETER TRACTABILITY 22
2.4.2 PARAMETERIZED HARDNESS 24
2.4.3 PROBLEM KERNELIZATION 24
2.4.4 LOWER BOUNDS ON THE PROBLEM KERNEL SIZE 25
2.5 FIXED-PARAMETER ALGORITHMS FOR GRAPHS OF BOUNDED TREEWIDTH ... 26
2.5.1 MONADIC SECOND-ORDER LOGIC 28
2.5.2 TREE AUTOMATA 29
3 JOB INTERVAL SELECTION AND 2-UNION INDEPENDENT SET 33
3.1 INTRODUCTION 34
3.1.1 KNOWN RESULTS 36
3.1.2 OUR RESULTS 37
XVII
HTTP://D-NB.INFO/1058974750
3.1.3 CHAPTER OUTLINE 39
3.2 COLORFUL INDEPENDENT SETS 40
3.2.1 A COLORFUL VERSION OF JOB INTERVAL SELECTION 40
3.2.2 COLORFUL INDEPENDENT SET WITH LISTS 42
3.2.3 ADVANTAGES AND LIMITATIONS OF THE MODEL 44
3.3 A COMPLEXITY DICHOTOMY 44
3.4 COMPACT INTERVAL GRAPHS 53
3.5 JOB INTERVAL SELECTION 57
3.5.1 A SIMPLE SEARCH TREE ALGORITHM 57
3.5.2 GENERALIZATIONS OF A KNOWN DYNAMIC PROGRAM 59
3.5.3 PROBLEM KERNELIZATION 67
3.6 2-UNION INDEPENDENT SET 72
3.6.1 A DYNAMIC PROGRAM FOR COMPACT INTERVAL GRAPHS 73
3.6.2 PROBLEM KERNELIZATION 74
3.7 EXPERIMENTAL EVALUATION 77
3.8 CONCLUSION 81
4 DAG PARTITIONING 83
4.1 INTRODUCTION 83
4.1.1 KNOWN RESULTS 84
4.1.2 OUR RESULTS 85
4.1.3 CHAPTER OUTLINE 86
4.2 THE STRUCTURE OF MINIMAL PARTITIONING SETS 86
4.3 FINDING CONSTANT-WEIGHT PARTITIONING SETS IN LINEAR TIME 88
4.3.1 A SEARCH TREE ALGORITHM 88
4.3.2 LINEAR-TIME DATA REDUCTION 92
4.3.3 LOWER BOUNDS 97
4.3.4 EXPERIMENTAL EVALUATION 105
4.4 LINEAR-TIME PARTITIONING TREE-LIKE GRAPHS 112
4.5 STRONGER NP-HARDNESS RESULTS 117
4.6 CONCLUSION 122
5 HITTING SET 123
5.1 INTRODUCTION 123
5.1.1 KNOWN RESULTS 124
5.1.2 OUR RESULTS 126
5.1.3 CHAPTER OUTLINE 126
5.2 EXPRESSIVE KERNELIZATION 126
XVIII
5.3 A LINEAR-TIME KERNELIZATION ALGORITHM 130
5.3.1 CORRECTNESS 132
5.3.2 PROBLEM KERNEL SIZE 134
5.3.3 RUNNING TIME 136
5.4 EXPERIMENTAL EVALUATION 138
5.5 REDUCING THE NUMBER OF VERTICES IN 0(A
15D
) ADDITIONAL TIME .... 145
5.5.1 THE APPROACHES OF ABU-KHZAM AND MOSER 145
5.5.2 OUR IMPROVEMENTS 147
5.6 CONCLUSION 150
6 HYPERGRAPH CUTWIDTH AND A GENERAL METHOD 151
6.1 INTRODUCTION 151
6.1.1 KNOWN RESULTS 154
6.1.2 OUR RESULTS 155
6.1.3 CHAPTER OUTLINE 155
6.2 A MYHILL-NERODE THEOREM FOR HYPERGRAPHS 155
6.2.1 REGULAR LANGUAGES 156
6.2.2 COLORED GRAPHS 156
6.2.3 HYPERGRAPHS 163
6.3 USING THE MYHILL-NERODE THEOREM 169
6.3.1 DERIVING FIXED-PARAMETER LINEAR-TIME ALGORITHMS 169
6.3.2 EXPRESSIBILITY IN MONADIC SECOND-ORDER LOGIC 171
6.4 HYPERGRAPH CUTWIDTH IS FIXED-PARAMETER LINEAR 173
6.4.1 HYPERGRAPH CUTWIDTH BOUNDS INCIDENCE TREEWIDTH 175
6.4.2 TESTS FOR CONSTANT CUTWIDTH 176
6.4.3 SHRINKING TESTS TO CONSTANT SIZE 181
6.5 HYPERTREE WIDTH AND VARIANTS 184
6.6 CONCLUSION 185
7 CONCLUSION AND OUTLOOK 187
BIBLIOGRAPHY 191
XIX
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| bvnumber | BV042337841 |
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| id | DE-604.BV042337841 |
| illustrated | Illustrated |
| indexdate | 2024-11-25T17:51:13Z |
| institution | BVB |
| isbn | 9783798327054 9783798327061 |
| language | English |
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| physical | XIX, 205 S. graph. Darst. |
| psigel | ebook |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Univ.-Verl. der TU Berlin |
| record_format | marc |
| series | Foundations of computing |
| series2 | Foundations of computing |
| spellingShingle | Bevern, René van Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations Foundations of computing Graph (DE-588)4021842-9 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Effizienter Algorithmus (DE-588)4125422-3 gnd Hypergraph (DE-588)4161063-5 gnd NP-hartes Problem (DE-588)4621705-8 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4134751-1 (DE-588)4125422-3 (DE-588)4161063-5 (DE-588)4621705-8 (DE-588)4113937-9 |
| title | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations |
| title_alt | Fixed-parameter linear-time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations |
| title_auth | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations |
| title_exact_search | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations |
| title_full | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations René van Bevern |
| title_fullStr | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations René van Bevern |
| title_full_unstemmed | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations René van Bevern |
| title_short | Fixed parameter linear time algorithms for NP-hard graph and hypergraph problems arising in industrial appliations |
| title_sort | fixed parameter linear time algorithms for np hard graph and hypergraph problems arising in industrial appliations |
| topic | Graph (DE-588)4021842-9 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Effizienter Algorithmus (DE-588)4125422-3 gnd Hypergraph (DE-588)4161063-5 gnd NP-hartes Problem (DE-588)4621705-8 gnd |
| topic_facet | Graph Berechnungskomplexität Effizienter Algorithmus Hypergraph NP-hartes Problem Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:kobv:83-opus4-55292 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027774432&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042337479 |
| work_keys_str_mv | AT bevernrenevan fixedparameterlineartimealgorithmsfornphardgraphandhypergraphproblemsarisinginindustrialappliations |