MPI-INF D1 Publications: Journal Article: Max-min online allocations with a reordering buffer

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Author, Editor(s)

Author(s):

Epstein, Leah
Levin, Asaf
van Stee, Rob

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Not MPG Author(s):

Epstein, Leah
Levin, Asaf

BibTeX cite key*:

EpLeSt11a

Title

Title*:	Max-min online allocations with a reordering buffer
Attachment(s):	bcover_jour2.dvi (115.57 KB); bcover_jour5_rev_sec.pdf (168.2 KB)

Journal

Journal Title*:	SIAM Journal on Discrete Mathematics	Journal's URL:	http://www.siam.org/journals/sidma.php
Download URL for the article:	http://dx.doi.org/10.1137/100794006	Language:	English

Publisher

Publisher's Name:	SIAM	Publisher's URL:	http://www.siam.org/
Publisher's Address:	Philadelphia, PA	ISSN:	0895-4801

Vol, No, pp, Date

Volume*:	25	Number:	3
Publishing Date:	2011
Pages*:	1230-1250	Number of VG Pages:	21
Page Start:	1230	Page End:	1250
Sequence Number:		DOI:	10.1137/100794006

Note, Abstract, ©

Note:
(LaTeX) Abstract:	We consider online scheduling so as to maximize the minimum load, using a reordering buffer which can store some of the jobs before they are assigned irrevocably to machines. For $m$ identical machines, we show an upper bound of $H_{m-1}+1$ for a buffer of size $m-1$. A competitive ratio below $H_m$ is not possible with any fixed buffer size, and it requires a buffer of size $\Omega(m/\log m)$ to get a ratio of $O(\log m)$. For uniformly related machines, we show that a buffer of size $m+1$ is sufficient to get a competitive ratio of $m$, which is best possible for any fixed sized buffer. We show similar results (but with different constructions) for the restricted assignment model. We give tight bounds for two machines in all the three models. These results sharply contrast to the (previously known) results which can be achieved without the usage of a reordering buffer, where it is not possible to get a ratio below a competitive ratio of $m$ already for identical machines, and it is impossible to obtain an algorithm of finite competitive ratio in the other two models, even for $m=2$. Our results strengthen the previous conclusion that a reordering buffer is a powerful tool and it allows a significant decrease in the competitive ratio of online algorithms for scheduling problems. Another interesting aspect of our results is that our algorithm for identical machines imitates the behavior of a greedy algorithm on (a specific set of) related machines, whereas our algorithm for related machines completely ignores the speeds until all jobs have arrived, and then only uses the relative order of the speeds.
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Correlation

MPG Unit:	Max-Planck-Institut für Informatik

MPG Subunit:	Algorithms and Complexity Group
Appearance:	MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@ARTICLE{EpLeSt11a,
AUTHOR = {Epstein, Leah and Levin, Asaf and van Stee, Rob},
TITLE = {Max-min online allocations with a reordering buffer},
JOURNAL = {SIAM Journal on Discrete Mathematics},
PUBLISHER = {SIAM},
YEAR = {2011},
NUMBER = {3},
VOLUME = {25},
PAGES = {1230--1250},
ADDRESS = {Philadelphia, PA},
ISBN = {0895-4801},
DOI = {10.1137/100794006},
}

Entry last modified by Anja Becker, 02/09/2012

Edit History (please click the blue arrow to see the details)

	Editor(s) [Library]	Created 12/09/2010 15:26:04
Revisions 4. 3. 2. 1. 0.	Editor(s) Anja Becker Rob van Stee Thomas Sauerwald Rob van Stee Rob van Stee	Edit Dates 09.02.2012 10:43:55 12/12/2011 04:02:36 PM 03/03/2011 05:58:17 PM 01-25-2011 15:08:38 12-09-2010 15:26:04

Attachment Section

bcover_jour2.dvi

bcover_jour5_rev_sec.pdf

bcover_jour2.dvi

bcover_jour5_rev_sec.pdf