Fault-Tolerant Search Algorithms Reliable Computation with Unreliable Information
This book examines approaches to fault-tolerance in the context of algorithmic search theory. It details the application of fault-tolerant search procedures to specific problems in distributed computing, bioinformatics and computational learning.
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Berlin, Heidelberg
Springer Nature
2013
Springer Springer Berlin / Heidelberg Springer Berlin Heidelberg |
| Edition | 1 |
| Series | Monographs in Theoretical Computer Science. An EATCS Series |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783642173271 3642173276 3642173268 9783642173264 |
| ISSN | 1431-2654 |
| DOI | 10.1007/978-3-642-17327-1 |
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| Abstract | This book examines approaches to fault-tolerance in the context of algorithmic search theory. It details the application of fault-tolerant search procedures to specific problems in distributed computing, bioinformatics and computational learning. |
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| AbstractList | This book examines approaches to fault-tolerance in the context of algorithmic search theory. It details the application of fault-tolerant search procedures to specific problems in distributed computing, bioinformatics and computational learning. Why a book on fault-tolerant search algorithms? Searching is one of the fundamental problems in computer science. Time and again algorithmic and combinatorial issues originally studied in the context of search find application in the most diverse areas of computer science and discrete mathematics. On the other hand, fault-tolerance is a necessary ingredient of computing. Due to their inherent complexity, information systems are naturally prone to errors, which may appear at any level - as imprecisions in the data, bugs in the software, or transient or permanent hardware failures. This book provides a concise, rigorous and up-to-date account of different approaches to fault-tolerance in the context of algorithmic search theory. Thanks to their basic structure, search problems offer insights into how fault-tolerant techniques may be applied in various scenarios. In the first part of the book, a paradigmatic model for fault-tolerant search is presented, the Ulam-Renyi problem. Following a didactic approach, the author takes the reader on a tour of Ulam-Renyi problem variants of increasing complexity. In the context of this basic model, fundamental combinatorial and algorithmic issues in the design of fault-tolerant search procedures are discussed. The algorithmic efficiency achievable is analyzed with respect to the statistical nature of the error sources, and the amount of information on which the search algorithm bases its decisions. In the second part of the book, more general models of faults and fault-tolerance are considered. Special attention is given to the application of fault-tolerant search procedures to specific problems in distributed computing, bioinformatics and computational learning. This book will be of special value to researchers from the areas of combinatorial search and fault-tolerant computation, but also to researchers in learning and coding theory, databases, and artificial intelligence. Only basic training in discrete mathematics is assumed. Parts of the book can be used as the basis for specialized graduate courses on combinatorial search, or as supporting material for a graduate or undergraduate course on error-correcting codes. |
| Author | Cicalese, Ferdinando |
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| Copyright | Springer-Verlag Berlin Heidelberg 2013 |
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| DOI | 10.1007/978-3-642-17327-1 |
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| ISSN | 1431-2654 |
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| Notes | Bibliography: p. 199-207 |
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| RelatedPersons | Rozenberg, Grzegorz Henzinger, Monika Salomaa, Arto Nielsen, Mogens Hromkovič, Juraj |
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| Snippet | This book examines approaches to fault-tolerance in the context of algorithmic search theory. It details the application of fault-tolerant search procedures to... Why a book on fault-tolerant search algorithms? Searching is one of the fundamental problems in computer science. Time and again algorithmic and combinatorial... |
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| SubjectTerms | Algorithms Computer algorithms Computer Science Data processing Computer science Fault-tolerant computing Querying (Computer science) Theory of Computation |
| Subtitle | Reliable Computation with Unreliable Information |
| TableOfContents | Intro -- Preface -- Acknowledgments -- Contents -- Chapter 1 Prologue: What This Book Is About -- 1.1 Part I: The Basic Model -- 1.1.1 Adaptive vs. Non-adaptive Search -- 1.1.2 Q-ary Search with Lies -- 1.1.3 Half-Lies, Erasures and Other Types of Errors -- 1.1.4 Heuristics -- 1.2 Part II: More Models and Applications -- 1.2.1 Erasure Errors, Delays and Time-outs -- 1.2.2 Group Testing -- 1.2.3 Memory Faults and Resilient Search -- 1.2.4 A Model of Learning -- 1.3 Bibliographic Notes -- Part I The Ulam-Rényi Game and Its Variants -- Chapter 2 Fault-Tolerant Search à la Ulam-Rényi -- 2.1 Introduction -- 2.1.1 The Binary Ulam-Rényi Game -- 2.2 The Volume Bound -- 2.3 Borderline States Satisfying the Volume Bound with Equality -- 2.4 The Solution of the 20 Question Game with Lies -- 2.5 Asymptotics for the Ulam-Rényi Problem -- 2.6 Heuristics for the Ulam-Rényi Problem -- Algorithm 1 -- Algorithm 2 -- 2.6.1 Experimental Validation of the Heuristics -- 2.7 Bibliographic Notes -- 2.8 Exercises -- Chapter 3 Adaptive vs. Non-adaptive Search -- 3.1 Coding in a Channel with Noiseless Feedback -- 3.2 No Feedback Equals Error-Correcting Codes -- 3.3 Elements of the Theory of Error-Correcting Codes -- 3.3.1 Linear and Hamming Codes -- 3.3.2 MDS Codes and the Reed-Solomon Codes -- 3.3.3 Bounds on Codes -- 3.4 Fault-Tolerant q-ary Search and Minimum Feedback -- 3.4.1 Fault-Tolerant q-ary search -- 3.4.2 Perfect Strategies and Least Adaptiveness: M=qm -- The Non-adaptive Second Batch of Questions -- Shrinking the First Batch of Questions -- 3.4.3 Arbitrary Cardinality of the Search Space: Least Adaptive Quasi-perfect Strategies -- More About Perfect Minimally Adaptive Strategies -- Quasi-perfect Strategies: The Main Theorem -- 3.5 Some Finite Exact Results for the q-ary Adaptive Ulam-Rényi game -- An Infinite Sequence of Winning States for q-ary Search Bounds for Two-Stage Algorithms with One Positive -- More Positives -- More Errors -- 7.3 Some Typical Applications of Group Testing in Computational Biology -- 7.4 Bibliographic Notes -- 7.5 Exercises -- Chapter 8 Resilient Search -- 8.1 The Definition of the Problem and a Lower Bound -- 8.2 Randomized Resilient Search -- 8.3 Optimal Deterministic Resilient Search -- 8.3.1 The Verification Procedure -- 8.4 Bibliographic Notes -- 8.5 Exercises -- Chapter 9 A Model for Learning -- 9.1 Computational Learning -- 9.2 Predicting from Expert Advice -- 9.3 Learning in Noisy Environments -- 9.3.1 Rényi's Probabilistic Example -- 9.3.2 Learning with Negative Reinforcement -- 9.3.3 Supervised Learning for Online Prediction -- 9.4 Bibliographic Notes -- 9.5 Exercises -- Bibliography Coping with Many Lies When M=qm -- 3.6 Bibliographic Notes -- 3.7 Exercises -- Chapter 4 Weighted Errors over a General Channel -- 4.1 Introduction -- 4.2 Two-Batch Search with Weighted Lies -- 4.3 The Lower Bound: The Winning Strategy -- 4.3.1 The First Batch of Questions -- 4.3.2 The Second Batch of Questions -- 4.4 The Upper Bound -- 4.5 Other Noise Models: Unidirectional Errors -- 4.6 Bibliographic Notes -- 4.7 Exercises -- Chapter 5 Variations on a Theme of Ulam and Rényi: More Types of Questions and Lies -- 5.1 Comparison-Based Search: The Multiple-Interval Queries -- 5.2 Query Optimal Multi-interval Search with k = O(e2) -- 5.2.1 The Case of Two Lies: A Canonical Representation of States and 2-Interval Queries -- 5.2.2 About Comparison Questions -- 5.3 Linearly Bounded Number of Lies -- 5.4 Prefix-Bounded Numbers of Lies -- 5.5 Bibliographic Notes -- 5.6 Exercises -- Part II Other Models -- Chapter 6 Delays and Time Outs -- 6.1 Search with Fixed Batches of Questions and Variable Delay in Answers -- 6.2 Search with Variable Batches and Delays -- 6.3 Lost Answers and Delays -- 6.3.1 Extensions and Generalizations -- 6.3.2 The Proof of Proposition 6.1 -- 6.3.3 Broadcast with Latency vs. Search with Delay -- Broadcast in the Postal Model -- Broadcast and Comparison Search Are Isomorphic Problems -- 6.4 Bibliographic Notes -- 6.5 Exercises -- Chapter 7 Group Testing -- 7.1 Group Testing with Subset Tests -- 7.1.1 The (p,v,n)-super-selector -- 7.1.2 Approximate Group Testing -- 7.1.3 Bounds on the Size of a (p, v, n)-super-selector -- 7.2 Interval Group Testing -- Sets of Queries and YES-Sets -- 7.2.1 Non-adaptive Fault-Tolerant Interval Group Testing -- 7.2.2 Two-Stage Fault-Tolerant Interval Group Testing -- An Averaging Argument for Lower Bound on Two-Stage Interval Group Testing -- The Averaging Argument in Use -- Yes-sets and Errors |
| Title | Fault-Tolerant Search Algorithms |
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