Englert, Matthias, Özmen, Deniz and Westermann, Matthias (2008) The power of reordering for online minimum makespan scheduling. In: 49th Annual IEEE Symposium on Foundations of Computer Science, Philadelphia, PA , 25-28 Oct 2008 . Published in: Symposium on Foundations of Computer Science. Annual Proceedings pp. 603-612.

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Abstract

In the classic minimum makespan scheduling problem, we are given an input sequence of jobs with processing times. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we do not require that each arriving job has to be assigned immediately to one of the machines. A reordering buffer with limited storage capacity can be used to reorder the input sequence in a restricted fashion so as to schedule the jobs with a smaller makespan. This is a natural extension of lookahead. We present an extensive study of the power and limits of online reordering for minimum makespan scheduling. As main result, we give, for m identical machines, tight and, in comparison to the problem without reordering, much improved bounds on the competitive ratio for minimum makespan scheduling with reordering buffers. Depending on m, the achieved competitive ratio lies between 4/3 and 1.4659. This optimal ratio is achieved with a buffer of size Theta(m). We show that larger buffer sizes do not result in an additional advantage and that a buffer of size Omega(m) is necessary to achieve this competitive ratio. Further, we present several algorithms for different buffer sizes. Among others, we introduce, for every buffer size k isin [1, (m+ 1)/2], a (2 middot 1/(m middot k+ 1))-competitive algorithm, which nicely generalizes the well-known result of Graham. For m uniformly related machines, we give a scheduling algorithm that achieves a competitive ratio of 2 with a reordering buffer of size m. Considering that the best knowncompetitive ratio for uniformly related machines without reordering is 5.828, this result emphasizes the power of online reordering further more.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Journal or Publication Title:	Symposium on Foundations of Computer Science. Annual Proceedings
Publisher:	IEEE Computer Society
ISSN:	1523-8288
Book Title:	2008 49th Annual IEEE Symposium on Foundations of Computer Science
Date:	2008
Page Range:	pp. 603-612
Identification Number:	10.1109/FOCS.2008.46
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Conference Paper Type:	Paper
Title of Event:	49th Annual IEEE Symposium on Foundations of Computer Science
Type of Event:	Other
Location of Event:	Philadelphia, PA
Date(s) of Event:	25-28 Oct 2008
URI:	http://wrap.warwick.ac.uk/id/eprint/42235

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