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 autoři: | , , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
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Washington, D.C
National Academy Press
1992
National Academies Press |
| Vydání: | 1 |
| Témata: | |
| ISBN: | 9780309047760, 0309047765 |
| On-line přístup: | Získat plný text |
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- 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