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Synopsis
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.
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Book Description
Randomization is one of the great resources in algorithm design and also one of its great mysteries. Although randomization seems to provide algorithms with more power, there is no proof that it is indeed the case. This book examines the discrepancy method, which may be the 'missing link' between randomness and complexity. The text discusses a selection of important topics illustrating the fruitfulness of this link. Several of the most exciting recent results in algorithms and complexity are covered, such as communication complexity, pseudo-randomness, rapidly mixing Markov chains, and multidimensional searching. With minimal pre-requisites, this book should appeal to students as well as researchers in computer science, operations research, pure and applied mathematics, and engineering.
Review
"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
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The Discrepancy Method: Randomness and Complexity
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Cambridge University Press (edition ), 2002
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The Discrepancy Method: Randomness and Complexity
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The Discrepancy Method: Randomness and Complexity
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The Discrepancy Method: Randomness and Complexity
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The Discrepancy Method: Randomness and Complexity
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The Discrepancy Method: Randomness and Complexity
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The Discrepancy Method (Paperback)
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Paperback. Condition: new. Paperback. 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. This book includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, derandomization, convex hulls and Voronoi diagrams, linear programming, geometric sampling and VC-dimension theory, and multidimensional searching. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521003575
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The Discrepancy Method: Randomness and Complexity
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