Probability And Computing: Randomized Algorithms And Probabi

Description:
Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, balls and bins models, the probabilistic method, and Markov chains. In the second half, the authors delve into more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods, coupling, martingales, and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

Review:
'This text provides a solid background in probabilistic techniques, illustrating each with well-chosen examples. The explanations are clear, and convey the intuition behind the results and techniques, yet the coverage is rigorous. An excellent advanced undergraduate text.' Peter Bartlett, Professor of Computer Science, University of California, Berkeley 'This book is suitable as a text for upper division undergraduates and first year graduate students in computer science and related disciplines. It will also be useful as a reference for researchers who would like to incorporate these tools into their work. I enjoyed teaching from the book and highly recommend it.' Valerie King, Professor of Computer Science, University of Victoria, British Columbia 'Buy it, read it, enjoy it; profit from it. it feels as if it has been well tested out of students and will work straight away.' Colin Cooper, Department of computer Science, King's College, University of London 'An exciting new book on randomized algorithms. It nicely covers all the basics, and also has some interesting modern applications for the more advanced student.' Alan Frieze, professor of Mathematics, Carnegie-Mellon University ' ... very well written and contains useful material on probability theory and its application in computer science.' Zentralblatt MATH ' ... this book offers a very good introduction to randomised algorithms and probabilistic analysis, both for the lecturer and independent reader alike. it is also a good book for those wanting practical examples that can be applied to real world problems.' Mathematics Today

Table of Contents:
Preface; 1. Events and probability; 2. Discrete random variables and expectation; 3. Moments and deviations; 4. Chernoff bounds; 5. Balls, bins and random graphs; 6. The probabilistic method; 7. Markov chains and random walks; 8. Continuous distributions and the Poisson process; 9. Entropy, randomness and information; 10. The Monte Carlo method; 11. Coupling of Markov chains; 12. Martingales; 13. Pairwise independence and universal hash functions; 14. Balanced allocations; References.

Author Biography:
Michael Miztenmacher is a John L. Loeb Associate Professor in Computer Science at Harvard University. Having written nearly 100 articles on a variety of topics in computer science, his research focuses on randomized algorithms and networks. He has received an NSF CAREER Award and an Alfred P. Sloan Research Fellowship. In 2002, he shared the IEEE Information Theory Society Best Paper Award for his work on error-correcting codes. Eli Upfal is Professor and Chair of Computer Science at Brown University. He has published more than 100 papers in refereed journals and professional conferences, and is the inventor of more than ten patents. His main research interests are randomized computation and probabilistic analysis of algorithms, with applications to optimization algorithms, communication networks, parallel and distributed computing and computational biology.