Online Scheduling on Identical Machines Using SRPT

Fox, Kyle J.

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https://hdl.handle.net/2142/18275 Copy

Description

Title

Online Scheduling on Identical Machines Using SRPT

Author(s)

Fox, Kyle J.

Issue Date

2011-01-14T22:43:35Z

Director of Research (if dissertation) or Advisor (if thesis)

Erickson, Jeff G.

Department of Study

Computer Science

Discipline

Computer Science

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• scheduling
• competitive analysis
• resource augmentation

Abstract

Due to its optimality on a single machine for the problem of minimizing average flow time, Shortest-Remaining-Processing-Time (SRPT) appears to be the most natural algorithm to consider for the problem of minimizing average flow time on multiple identical machines. It is known that SRPT achieves the best possible competitive ratio on multiple machines up to a constant factor. Using resource augmentation, SRPT is known to achieve total flow time at most that of the optimal solution when given machines of speed $2- 1/m$. Further, it is known that SRPT's competitive ratio improves as the speed increases; SRPT is $s$-speed $1/s$-competitive when $s \geq 2 - 1/m$. However, a gap has persisted in our understanding of SRPT. Before this work, we did not know the performance of SRPT when given machines of speed $1+\eps$ for any $0 < \eps < 1 - 1/m$. We answer the question in this thesis. We show that SRPT is scalable on $m$ identical machines. That is, we show SRPT is $(1+\eps)$-speed $O(1/\eps)$-competitive for any $\eps > 0$. We also show that SRPT is $(1+\eps)$-speed $O(1/\eps^2)$-competitive for the objective of minimizing the $l_k$ norms of flow time on $m$ identical machines. Both of our results rely on new potential functions that capture the structure of SRPT. Our results, combined with previous work, show that SRPT is the best possible online algorithm in essentially every aspect when migration is permissible.

Graduation Semester

2010-12

Permalink

http://hdl.handle.net/2142/18275

Copyright and License Information

Copyright 2010 Kyle J. Fox

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