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Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

Shakhlevich, N.V., Shioura, A. and Strusevich, V.A. (2008) Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach. In: Algorithms - ESA 2008 : 16th Annual European Symposium, Karlsruhe, Germany, September 15-17, 2008. Proceedings. Lecture Notes in Computer Science (5193). Springer , pp. 756-767. ISBN 1611-3349

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Abstract

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper.

Item Type: Book Section
Copyright, Publisher and Additional Information: © 2008 Springer. This is an author produced version of a paper published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self archiving policy.
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 22 Jan 2009 12:51
Last Modified: 08 Feb 2013 17:05
Published Version: http://dx.doi.org/10.1007/978-3-540-87744-8_63
Status: Published
Publisher: Springer
Refereed: Yes
Identification Number: 10.1007/978-3-540-87744-8_63
URI: http://eprints.whiterose.ac.uk/id/eprint/5397

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