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The Nature of Computation$
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Cristopher Moore and Stephan Mertens

Print publication date: 2011

Print ISBN-13: 9780199233212

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199233212.001.0001

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Randomized Algorithms

Randomized Algorithms

(p.450) (p.451) Chapter 10 Randomized Algorithms
The Nature of Computation

Cristopher Moore

Stephan Mertens

Oxford University Press

Certain situations require a random rather than a deterministic strategy. With a random strategy, the choices are unpredictable and the adversary may be kept off balance. This chapter focuses on the variety and power of randomised algorithms. More specifically, it considers algorithms that find the smallest cut in a graph by combining random vertices until only two remain, or play games by searching the tree of possible moves in random order. It also explains how to check whether the software on a space probe is uncorrupted, how to turn a puzzle with many solutions into one with a unique solution, and how to determine whether two functions are equal. It describes tools such as random hash functions and polynomial identity testing, analyzes the nature of the primes, and looks at a series of randomised algorithms for primality based on different number-theoretic ideas. The chapter concludes by discussing several complexity classes consisting of problems that can be solved using various kinds of randomized algorithms in polynomial time.

Keywords:   randomised algorithms, solutions, random hash functions, polynomial identity testing, primes, primality, games, complexity classes, polynomial time

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