Probability and algorithms

Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to them. Concepts from the field of probability are also increasingly useful in analyzing the performance of algorithms, broadening our understa...

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Hlavní autori: Council, National Research, Sciences, Division on Engineering and Physical, Commission on Physical Sciences, Mathematics, and Applications, Algorithms, Panel on Probability and
Médium: E-kniha Kniha
Jazyk:English
Vydavateľské údaje: Washington, D.C National Academy Press 1992
National Academies Press
Vydanie:1
Predmet:
Algorithms
Probabilities
ISBN:9780309047760, 0309047765
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Abstract Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to them. Concepts from the field of probability are also increasingly useful in analyzing the performance of algorithms, broadening our understanding beyond that provided by the worst-case or average-case analyses.This book surveys both of these emerging areas on the interface of the mathematical sciences and computer science. It is designed to attract new researchers to this area and provide them with enough background to begin explorations of their own.
AbstractList Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to them. Concepts from the field of probability are also increasingly useful in analyzing the performance of algorithms, broadening our understanding beyond that provided by the worst-case or average-case analyses.This book surveys both of these emerging areas on the interface of the mathematical sciences and computer science. It is designed to attract new researchers to this area and provide them with enough background to begin explorations of their own.
Author National Research Council (U.S.). Panel on Probability and Algorithms
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Notes Includes bibliographical references
OCLC 923264223
PQID EBC3376511
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Snippet Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to...
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SubjectTerms Algorithms
Probabilities
TableOfContents PROBABILITY AND ALGORITHMS -- Copyright -- Preface -- Contents -- 1. Introduction -- 1.1 PROBABILISTIC ALGORITHMS -- 1.1.1 Everyday Examples -- 1.1.2 Hashing -- 1.1.3 Geometry -- 1.1.4 Competitive Analysis -- 1.1.5 Random Constructions -- 1.1.6 Testing Equality and Faith -- 1.2 PROBABILISTIC ANALYSIS OF ALGORITHMS -- 1.2.1 Sample Analyses: The Assignment Problem -- 1.2.2 Quick Lessons from Quicksort -- 1.3 HOW TO USE THIS SURVEY -- REFERENCES -- 2. Simulated Annealing -- ABSTRACT -- 2.1 THE METHOD -- 2.2 CONVERGENCE ANALYSIS -- 2.2.1 Basic Results -- 2.2.2 Taking the Instance Size into Account -- 2.3 BEHAVIOR IN PRACTICE -- REFERENCES -- 3. Approximate Counting Via Markov Chains -- ABSTRACT -- 3.1 EXACT AND APPROXIMATE COUNTING -- 3.2 RECURSIVE ESTIMATION OF SIZE -- 3.3 THE MARKOV CHAIN METHOD OF SIMULATING A PROBABILITY DISTRIBUTION -- 3.4 ESTIMATING MIXING TIMES -- 3.5 CONCLUSION -- REFERENCES -- 4. Probabilistic Algorithms for Speedup -- ABSTRACT -- 4.1 INTRODUCTION -- 4.2 PROBABILISTIC COMPLEXITY CLASSES -- 4.3 PROBABILISTIC ALGORITHMS IN NUMBER THEORY: FACTORING AND PRIMALITY TESTING -- Miller's Primality Test -- Solovay-Strassen Primality Test -- Dixon's Random Squares Factoring Algorithm -- 4.4 COMMUNICATION COMPLEXITY -- Randomized Prime Protocol -- Repeated Equality Protocol -- REFERENCES -- 5. Probabilistic Algorithms for Defeating Adversaries -- ABSTRACT -- 5.1 INTRODUCTION -- 5.2 EXAMPLES -- 5.2.1 Authentication -- 5.2.2 Computing with Encrypted Data -- 5.3 ZERO-KNOWLEDGE PROOF SYSTEMS AND INSTANCE-HIDING SCHEMES -- REFERENCES -- 6. Pseudorandom Numbers -- ABSTRACT -- 6.1 INTRODUCTION -- 6.2 EXPLICIT CONSTRUCTIONS OF PSEUDORANDOM BIT GENERATORS -- 6.3 COMPUTATIONAL INFORMATION THEORY AND CRYPTOGRAPHY -- 6.4 PERFORMANCE OF CERTAIN PSEUDORANDOM BIT GENERATORS -- REFERENCES
11.1.3 Multibutterflies -- 11.1.4 Expansion -- 11.1.5 History -- 11.1.6 Outline -- 11.2 PACKET SWITCHING -- 11.3 CIRCUIT SWITCHING -- 11.3.1 Unique Neighbors -- 11.3.2 The Algorithm -- 11.4 FAULT TOLERANCE -- 11.5 NONBLOCKING NETWORKS -- REFERENCES -- 12. Missing Pieces, Derandomization, and Concluding Remarks -- REFERENCES
7. Probabilistic Analysis of Packing and Related Partitioning Problems -- ABSTRACT -- 7.1 INTRODUCTION -- 7.1.1 Problems -- 7.1.2 Analysis -- 7.1.3 Bp Algorithms -- 7.1.4 Ms Algorithms -- 7.2 ANALYTICAL TECHNIQUES -- 7.2.1 Markov Chains -- 7.2.2 Bounds -- 7.2.3 Stochastic Planar Matching -- 7.2.4 Linear Programming -- 7.3 RELATED TOPICS -- 7.3.1 Variants -- 7.3.2 Higher Dimensions -- 7.3.3 General Bounds -- 7.3.4 Distributions -- 7.4 DIRECTIONS FOR FURTHER STUDY -- REFERENCES -- 8. Probability and Problems in Euclidean Combinatorial Optimization -- ABSTRACT -- 8.1 INTRODUCTION -- 8.2 SUBADDITIVE EUCLIDEAN FUNCTIONALS -- 8.3 TAIL PROBABILITIES -- 8.4 THE TSP IN FRACTAL SPACES -- 8.5 MINIMAL SPANNING TREES -- 8.6 MATCHING PROBLEMS -- 8.7 THE VALUES OF THE CONSTANTS -- 8.8 THE CENTRAL LIMIT PROBLEM -- 8.9 WORST-CASE GROWTH RATES -- 8.10 CONCLUDING REMARKS -- REFERENCES -- 9. Probabilistic Analysis in Linear Programming -- ABSTRACT -- 9.1 THE LINEAR PROGRAMMING PROBLEM -- 9.2 PROBABILISTIC ANALYSIS -- 9.2.1 Parametric Simplex Variants -- 9.2.2 Borgwardt's Results -- 9.2.3 Asymptotic Results: Smale and Others -- 9.2.4 Adler, Haimovich: Sign-Invariant Model for Phase II -- 9.2.5 The Quadratic Results -- 9.3 RANDOMIZED ALGORITHMS -- 9.4 THE ROAD AHEAD -- REFERENCES -- 10. Randomization in Parallel Algorithms -- ABSTRACT -- 10.1 INTRODUCTION -- 10.2 QUALITY MEASURES FOR RANDOMIZED PARALLEL ALGORITHMS -- 10.3 THE RANDOMIZED PARALLEL COMPLEXITY CLASS RNC -- 10.4 SOME IMPORTANT PROBLEMS IN RNC -- 10.4.1 Testing if a Multivariate Polynomial is not Identically Zero -- 10.4.2 Finding a Maximum Matching in a Graph -- 10.5 RANDOMIZATION LEADS TO SIMPLE PARALLEL ALGORITHMS -- 10.6 ELIMINATING RANDOMIZATION -- 10.7 CONCLUSION -- REFERENCES -- 11. Randomly Wired Multistage Networks -- ABSTRACT -- 11.1 INTRODUCTION -- 11.1.1 Dilated Butterflies -- 11.1.2 Delta Networks
Title Probability and algorithms
URI https://cir.nii.ac.jp/crid/1130000793659540096
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