The Discrepancy Method
The Discrepancy Method
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The discrepancy method has produced the most fruitful line of attack on a pivotal computer science question: 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 http://www.cs.princeton.edu/~chazelle/book.html.
- Several of the most exciting recent results in algorithms and complexity are covered
- Self-contained, with much of the mathematical background provided. Chapters are mostly independent, so the book can be used as reference.
- A potential classic along the lines of The Probabilistic Method by Alon and Spencer (published by Wiley)
Reviews & endorsements
"Chazelle writes well, treats the reader generously, and works passionately to find the common threads in a plethora of important, late-breaking developments at the crossroads of mathematics and computer science. Both as personal testament and crafted exposition, this invitation into ongoing research reads with the feel of an intimate audience with an enthusiastic leading expert. Upper division undergraduates through professionals." Choice
Product details
July 2000Hardback
9780521770934
494 pages
229 × 152 × 32 mm
0.89kg
160 b/w illus.
Available
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.
