Randomized algorithms for on-line scheduling problems: how low can't you go?

Authors:
Leen Stougie;Arjen P. A. Vestjens
Affiliations:
Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Den Dolech 2, 5600 MB Eindhoven, and CWI, Amsterdam, The Netherlands;Center for Quantitative Methods (CQM), Eindhoven, The Netherlands
Venue:
Operations Research Letters
Year:
2002

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Abstract

We prove lower bounds on the competitive ratio of randomized algorithms for several on-line scheduling problems. The main result is a bound of e/(e-1) for the on-line problem with objective minimizing the sum of completion times of jobs that arrive over time at their release times and are to be processed on a single machine. This lower bound shows that a randomized algorithm designed in Chekuri et al. (Proceedings of the Eighth ACM-SIAM Symposium on Discrete Algorithms, 1997, 609-618) is a best possible randomized algorithm for this problem.