The Discrepancy Method: Randomness and Complexity - Hardcover

Chazelle, Bernard

Hardcover

ISBN 10: 0521770939 ISBN 13: 9780521770934

Publisher: Cambridge University Press, 2000

Synopsis

The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal to students and researchers in computer science, operations research, pure and applied mathematics, and engineering.

About this title

Review

'Bernard Chazelle's book The Discrepancy Method is a technical tour de force ... this is an eminently readable book.' Prabhakar Raghavan, SIAM Review

' ... the main point is that by presenting the discrepancy method in such an impressive way as this book does, the author helps us to imagine the fantastic possibilities that randomization opens up to everybody, and he shows that current research in theoretical computer science has an astonishing impact on common fundamentals of all sciences. I believe that any reader interested in principal questions will enjoy this book.' The Computer Journal

Book Description

The discrepancy method is the most fruitful line of attack on the pivotal question: what is the computational power of random bits? This book includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, derandomization, convex hulls and Voronoi diagrams, linear programming, geometric sampling and VC-dimension theory, and multidimensional searching.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2000
• Language: English
• ISBN 10: 0521770939
• ISBN 13: 9780521770934
• Binding: Hardcover
• Number of pages: 494