Optimal speedup of Las Vegas algorithms

• Published in: Information processing letters Vol. 47; no. 4; pp. 173 - 180
• Main Authors: Luby, Michael, Sinclair, Alistair, Zuckerman, David
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 27.09.1993; Elsevier Science
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Design of algorithms; Exact sciences and technology; expected running time; Las Vegas algorithms; optimal strategy; proof search; randomized algorithms; theorem-proving; Theoretical computing; Design of algorithms; theorem-proving; randomized algorithms; Las Vegas algorithms; proof search; optimal strategy; expected running time; Design algorithm; Optimal strategy; Theorem proving; Algorithmics; Las Vegas algorithm; Randomized algorithm; Expected running time; Proof search; Programming theory
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/0020-0190(93)90029-9

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 scL = ( t 1, t 2,…) be a strategy, and let l A = inf scL T( A, scL), where T( A, scL) i s the expected value of the running time of the simulation of A under strategy scL. We describe a simple universal strategy scL univ, with the property that, for any algorithm A, T( A, scL univ) = O( lin A log( linA)). Furthermore, we show that this is the best performance that can be achieved, up to a constant factor, by any universal strategy.