The discrepancy method : randomness and complexity / Bernard Chazelle.
By: Chazelle, B. (Bernard) [author]
Language: English Publisher: Cambridge: Cambridge University Press, c2013Description: 1 online resource (xvii, 463 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9780511626371Subject(s): Irregularities of distribution (Number theory) | Random variables | Computational complexityGenre/Form: Electronic books.DDC classification: 512.7 Online resources: Full text available at Cambridge University Press Click here to view Summary: 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.| Item type | Current location | Home library | Call number | Status | Date due | Barcode | Item holds |
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COLLEGE LIBRARY | COLLEGE LIBRARY LIC Gateway | 512.7 C399 2013 (Browse shelf) | Available | CL-46226 |
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| 512.2 H888 2012 Numbers, groups, and codes / J.F. Humphreys, M.Y. Prest. | 512.5 C733 2013 Combinatorial and geometric group theory : Edinburgh, 1993 / | 512.5 Os72 2012 Advanced mathematical methods / | 512.7 C399 2013 The discrepancy method : randomness and complexity / | 512.7 N917 2012 Number theory and cryptography / | 512.8 23 Core concepts in mathematics: set theory | 512.9 D878 2000 Intermediated algebra / |
Includes bibliographical references and index.
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.
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