The Discrepancy Method: Randomness and Complexity

by Bernard Chazelle

The discrepancy method has produced the most fruitful line of attack on a pivotal computer science What is the computational power of random bits? It has also played a major role in recent developments in complexity theory. This book tells the story of the discrepancy method in a few succinct independent vignettes. The chapters explore such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on a sphere, derandomization, convex hulls and Voronoi diagrams, linear programming, geometric sampling and VC-dimension theory, minimum spanning trees, circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained, with minimal prerequisites. More information can be found on the book's home page at

494 pages, Paperback

First published December 15, 2001