Bernard ChazelleCambridge University Press, 10/5/2000EAN 9780521770934, ISBN10: 0521770939Hardcover, 494 pages, 22.9 x 15.2 x 3.3 cmLanguage: EnglishThe 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.1. Combinatorial discrepancy2. Upper bounds in geometric discrepancy3. Lower bounds in geometric discrepancy4. Sampling5. Geometric searching6. Complexity lower bounds7. Convex hulls and Voronoi diagrams8. Linear programming and extensions9. Pseudo-randomness10. Communication complexity11. Minimum spanning treesA. Probability theoryB. Harmonic analysisC. Convex geometry.
