Randomized Algorithms

This book presents basic tools from probability theory used in algorithmic applications, with concrete examples.

Rajeev Motwani (Author), Prabhakar Raghavan (Author)

9780521474658, Cambridge University Press

Hardback, published 25 August 1995

496 pages
26.2 x 18.3 x 3.2 cm, 1.031 kg

'This book can serve as an excellent basis for a graduate course. It is highly recommended for students and researchers who wish to deepen their knowledge of the subject. Finally, I believe that the book, with its vast coverage, will be an invaluable source for active researchers in the field.' Y. Aumann, Computing Reviews

For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.

Part I. Tools and Techniques: 1. Introduction
2. Game-theoretic techniques
3. Moments and deviations
4. Tail inequalities
5. The probabilistic method
6. Markov chains and random walks
7. Algebraic techniques
Part II. Applications: 8. Data structures
9. Geometric algorithms and linear programming
10. Graph algorithms
11. Approximate counting
12. Parallel and distributed algorithms
13. Online algorithms
14. Number theory and algebra
Appendix A: notational index
Appendix B: mathematical background
Appendix C: basic probability theory.

Subject Areas: Computer science [UY], Algorithms & data structures [UMB]