Design and analysis of randomized algorithms: introduction to design paradigms
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
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| Series: | Texts in theoretical computer science
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 267 - 269 |
| Physical Description: | XII, 274 S. graph. Darst. 24 cm |
| ISBN: | 9783540239499 3540239499 |
Staff View
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| 245 | 1 | 0 | |a Design and analysis of randomized algorithms |b introduction to design paradigms |c J. Hromkovič |
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Record in the Search Index
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| adam_text | Contents 1 Introduction........................................................................................... 1 1.1 What Is Randomness and Does There Exist True Randomness? ....................................................................... 1 1.2 Randomness as a Source of Efficiency an Exemplary Application........................................................... 5 1.3 Concept of the Book..................................................................... 11 1.4 To the Student.............................................................................. 14 1.5 To the Teacher.............................................................................. 16 2 Fundamentals.......................................................................................... 19 2.1 2.2 2.3 2.4 2.5 Objectives...................................................................................... Elementary Probability Theory................................................... Models of Randomized Algorithms.............................................. Classification of Randomized Algorithms.................................. Classification of Randomized Algorithms for Optimization Problems........................................................... 2.6 Paradigms of the Design of Randomized Algorithms............... 2.7 Summary........................................................................................ 3 72 87 96 Foiling the Adversary........................................................................... 101 3.1 3.2 3.3 3.4 3.5 3.6 4 19 20 37 51
Objectives....................................................................................... 101 Hashing........................................................................................... 102 Universal Hashing..........................................................................109 Online Algorithms..........................................................................116 Randomized Online Algorithms...................................................120 Summary......................................................................................... 128 Fingerprinting.........................................................................................131 4.1 Objectives....................................................................................... 131 4.2 Communication Protocols.............................................................133 4.3 The Substring Problem.................................................................. 139
XII Contents 4.4 Verification of Matrix Multiplication........................................... 141 4.5 Equivalence of Two Polynomials................................................... 144 4.6 Summary......................................................................................... 149 5 Success Amplification and RandomSampling............................153 5.1 Objectives....................................................................................... 153 5.2 Efficient Amplification by Repeating Critical Computation Parts...........................................................154 5.3 Repeated Random Sampling and Satisfiability............................ 166 5.4 Random Sampling and Generating Quadratic Nonresidues .... 174 5.5 Summary......................................................................................... 181 6 Abundance of Witnesses.................................................................. 183 6.1 Objectives....................................................................................... 183 6.2 Searching for Witnesses for PrimalityTesting............................. 184 6.3 Solovay-Strassen Algorithm for Primality Testing...................... 192 6.4 Generation of Random Primes..................................................... 202 6.5 Summary......................................................................................... 206 7 Optimization and Random Rounding..........................................209 7.1 Objectives....................................................................................... 209
7.2 Relaxation to Linear Programming............................................. 210 7.3 Random Rounding and MAX-SAT............................................... 216 7.4 Combining Random Sampling and RandomRounding................ 222 7.5 Summary........................................................................ 225 A Fundamentals of Mathematics........................................................227 A.l Objectives...................................................................................... 227 A.2 Algebra and Number Theory....................................................... 228 A.3 Combinatorics ...............................................................................256 A.4 Summary........................................................................................ 264 References................................................................................................... 267 Index 271
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| adam_txt |
Contents 1 Introduction. 1 1.1 What Is Randomness and Does There Exist True Randomness? . 1 1.2 Randomness as a Source of Efficiency an Exemplary Application. 5 1.3 Concept of the Book. 11 1.4 To the Student. 14 1.5 To the Teacher. 16 2 Fundamentals. 19 2.1 2.2 2.3 2.4 2.5 Objectives. Elementary Probability Theory. Models of Randomized Algorithms. Classification of Randomized Algorithms. Classification of Randomized Algorithms for Optimization Problems. 2.6 Paradigms of the Design of Randomized Algorithms. 2.7 Summary. 3 72 87 96 Foiling the Adversary. 101 3.1 3.2 3.3 3.4 3.5 3.6 4 19 20 37 51
Objectives. 101 Hashing. 102 Universal Hashing.109 Online Algorithms.116 Randomized Online Algorithms.120 Summary. 128 Fingerprinting.131 4.1 Objectives. 131 4.2 Communication Protocols.133 4.3 The Substring Problem. 139
XII Contents 4.4 Verification of Matrix Multiplication. 141 4.5 Equivalence of Two Polynomials. 144 4.6 Summary. 149 5 Success Amplification and RandomSampling.153 5.1 Objectives. 153 5.2 Efficient Amplification by Repeating Critical Computation Parts.154 5.3 Repeated Random Sampling and Satisfiability. 166 5.4 Random Sampling and Generating Quadratic Nonresidues . 174 5.5 Summary. 181 6 Abundance of Witnesses. 183 6.1 Objectives. 183 6.2 Searching for Witnesses for PrimalityTesting. 184 6.3 Solovay-Strassen Algorithm for Primality Testing. 192 6.4 Generation of Random Primes. 202 6.5 Summary. 206 7 Optimization and Random Rounding.209 7.1 Objectives. 209
7.2 Relaxation to Linear Programming. 210 7.3 Random Rounding and MAX-SAT. 216 7.4 Combining Random Sampling and RandomRounding. 222 7.5 Summary. 225 A Fundamentals of Mathematics.227 A.l Objectives. 227 A.2 Algebra and Number Theory. 228 A.3 Combinatorics .256 A.4 Summary. 264 References. 267 Index 271 |
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| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
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| index_date | 2024-07-02T13:24:53Z |
| indexdate | 2024-07-09T20:27:03Z |
| institution | BVB |
| isbn | 9783540239499 3540239499 |
| language | English |
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| physical | XII, 274 S. graph. Darst. 24 cm |
| publishDate | 2005 |
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| spelling | Hromkovič, Juraj 1958- Verfasser (DE-588)123212898 aut Design and analysis of randomized algorithms introduction to design paradigms J. Hromkovič Berlin [u.a.] Springer 2005 XII, 274 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Literaturverz. S. 267 - 269 Algorithmes Analyse (wiskunde) gtt Processus stochastiques Random walks (statistiek) gtt Algorithms Stochastic processes Randomisierter Algorithmus (DE-588)4176929-6 gnd rswk-swf Randomisierter Algorithmus (DE-588)4176929-6 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014189267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hromkovič, Juraj 1958- Design and analysis of randomized algorithms introduction to design paradigms Algorithmes Analyse (wiskunde) gtt Processus stochastiques Random walks (statistiek) gtt Algorithms Stochastic processes Randomisierter Algorithmus (DE-588)4176929-6 gnd |
| subject_GND | (DE-588)4176929-6 |
| title | Design and analysis of randomized algorithms introduction to design paradigms |
| title_auth | Design and analysis of randomized algorithms introduction to design paradigms |
| title_exact_search | Design and analysis of randomized algorithms introduction to design paradigms |
| title_exact_search_txtP | Design and analysis of randomized algorithms introduction to design paradigms |
| title_full | Design and analysis of randomized algorithms introduction to design paradigms J. Hromkovič |
| title_fullStr | Design and analysis of randomized algorithms introduction to design paradigms J. Hromkovič |
| title_full_unstemmed | Design and analysis of randomized algorithms introduction to design paradigms J. Hromkovič |
| title_short | Design and analysis of randomized algorithms |
| title_sort | design and analysis of randomized algorithms introduction to design paradigms |
| title_sub | introduction to design paradigms |
| topic | Algorithmes Analyse (wiskunde) gtt Processus stochastiques Random walks (statistiek) gtt Algorithms Stochastic processes Randomisierter Algorithmus (DE-588)4176929-6 gnd |
| topic_facet | Algorithmes Analyse (wiskunde) Processus stochastiques Random walks (statistiek) Algorithms Stochastic processes Randomisierter Algorithmus |
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