A 3/2-approximation algorithm for rate-monotonic multiprocessor scheduling of implicit-deadline tasks

Authors:
Andreas Karrenbauer;Thomas Rothvoß
Affiliations:
Zukunftskolleg, University of Konstanz, Germany;Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Venue:
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Year:
2010

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Abstract

We present a new approximation algorithm for rate-monotonic multiprocessor scheduling of periodic tasks with implicit deadlines. We prove that for an arbitrary parameter k ∈ N it yields solutions with at most (3/2 + 1/k)OPT+9k many processors, thus it gives an asymptotic 3/2-approximation algorithm. This improves over the previously best known ratio of 7/4. Our algorithm can be implemented to run in time O(n2), where n is the number of tasks. It is based on custom-tailored weights for the tasks such that a greedy maximal matching and subsequent partitioning by a first-fit strategy yields the result.