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    612-822-4611

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Probabilistic Methods for Algorithmic Discrete Mathematics

Probabilistic Methods for Algorithmic Discrete Mathematics

McDiarmid, Colin
Ramirez-Alfonsin, Jorge
Habib, Michel

Paperback

Series: Algorithms and Combinatorics, Book 16

General ComputersGeneral MathematicsProbability & Statistics

ISBN10: 3642084265
ISBN13: 9783642084263
Publisher: Springer
Published: Aug 18 2010
Pages: 325
Weight: 1.06
Height: 0.72 Width: 6.14 Depth: 9.21
Language: English
Leave nothing to chance. This cliche embodies the common belief that ran- domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba- bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus- sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech- niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) o.

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