Optimal Speedup of Las Vegas Algorithms (1993)
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| Venue: | Information Processing Letters |
| Citations: | 86 - 0 self |
BibTeX
@ARTICLE{Luby93optimalspeedup,
author = {Michael Luby and Alistair Sinclair and David Zuckerman},
title = {Optimal Speedup of Las Vegas Algorithms},
journal = {Information Processing Letters},
year = {1993},
volume = {47},
pages = {173--180}
}
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Abstract
Let A be a Las Vegas algorithm, i.e., A is a randomized algorithm that always produces the correct answer when it stops but whose running time is a random variable. We consider the problem of minimizing the expected time required to obtain an answer from A using strategies which simulate A as follows: run A for a fixed amount of time t 1 , then run A independently for a fixed amount of time t 2 , etc. The simulation stops if A completes its execution during any of the runs. Let S = (t 1 ; t 2 ; : : :) be a strategy, and let ` A = inf S T (A; S) , where T (A; S) is the expected value of the running time of the simulation of A under strategy S . We describe a simple universal strategy S univ , with the property that, for any algorithm A , T (A; S univ ) = O(`A log(` A )) . Furthermore, we show that this is the best performance that can be achieved, up to a constant factor, by any universal strategy. Keywords: Design of algorithms, randomized algorithms, Las Vegas algorithms, expe...
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