NDLI: SRPT optimally utilizes faster machines to minimize flow time

Content Provider	ACM Digital Library
Author	Torng, Eric Mccullough, Jason
Copyright Year	2008
Abstract	We analyze the shortest remaining processing time (SRPT) algorithm with respect to the problem of scheduling $\textit{n}$ jobs with release times on $\textit{m}$ identical machines to minimize total flow time. It is known that SRPT is optimal if $\textit{m}$ = 1 but that SRPT has a worst-case approximation ratio of Θ(min(log $\textit{n/m},$ log Δ)) for this problem, where Δ is the ratio of the length of the longest job divided by the length of the shortest job. It has previously been shown that SRPT is able to use faster machines to produce a schedule as good as an optimal algorithm using slower machines. We now show that SRPT $\textit{optimally}$ uses these faster machines with respect to the worst-case approximation ratio. That is, if SRPT is given machines that are $\textit{s}$ ≥ 2 ™ $1/\textit{m}$ times as fast as those used by an optimal algorithm, SRPT's flow time is at least s times smaller than the flow time incurred by the optimal algorithm. Clearly, no algorithm can offer a better worst-case guarantee, and we show that existing algorithms with similar performance guarantees to SRPT without resource augmentation do not optimally use extra resources.
Starting Page	1
Ending Page	25
Page Count	25
File Format	PDF
ISSN	15496325
e-ISSN	15496333
DOI	10.1145/1435375.1435376
Volume Number	5
Issue Number	1
Journal	ACM Transactions on Algorithms (TALG)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-12-12
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	SRPT Flow time Parallel machines Resource augmentation Scheduling
Content Type	Text
Resource Type	Article
Subject	Mathematics

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