The Discrepancy Method
Randomness and Complexity
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64 274 Ft
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Product details:
- Publisher Cambridge University Press
- Date of Publication 24 July 2000
- ISBN 9780521770934
- Binding Hardback
- No. of pages494 pages
- Size 229x152x32 mm
- Weight 890 g
- Language English
- Illustrations 160 b/w illus. 0
Categories
Short description:
Explores the link between discrepancy theory and randomized algorithms.
MoreLong description:
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.
'Bernard Chazelle's book The Discrepancy Method is a technical tour de force ... this is an eminently readable book.' Prabhakar Raghavan, SIAM Review
Table of Contents:
1. Combinatorial discrepancy; 2. Upper bounds in geometric discrepancy; 3. Lower bounds in geometric discrepancy; 4. Sampling; 5. Geometric searching; 6. Complexity lower bounds; 7. Convex hulls and Voronoi diagrams; 8. Linear programming and extensions; 9. Pseudo-randomness; 10. Communication complexity; 11. Minimum spanning trees; A. Probability theory; B. Harmonic analysis; C. Convex geometry.
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