Abstract
A randomized algorithm makes random choices during its execution. The behavior of such an algorithm may thus be random even on a fixed input. The process of designing and analyzing a randomized algorithm focuses on establishing that it is likely to behave “well” on every input. The likelihood in such a statement depends only on the probabilistic choices made by the algorithm during execution and not on any assumptions about the input. It is especially important to distinguish a randomized algorithm from the averagecase analysis of algorithms, where one analyzes an algorithm assuming that its input is drawn from a fixed probability distribution. With a randomized algorithm, in contrast, no assumption is made about the input.
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Supported by an Alfred P. Sloan Research Fellowship, an IBM Faculty Partnership Award, an ARO MURI Grant DAAH04-96-1-0007, and NSF Young Investigator Award CCR-9357849, with matching funds from IBM, Schlumberger Foundation, Shell Foundation, and Xerox Corporation.
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Motwani, R., Raghavan, P. (1998). An Overview of Randomized Algorithms. In: Habib, M., McDiarmid, C., Ramirez-Alfonsin, J., Reed, B. (eds) Probabilistic Methods for Algorithmic Discrete Mathematics. Algorithms and Combinatorics, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12788-9_3
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