NDLI: Max-min Online Allocations with a Reordering Buffer

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Epstein, Leah Levin, Asaf van Stee, Rob
Copyright Year	2011
Abstract	We consider online scheduling so as to maximize the minimum load, using a reordering buffer that can store some of the jobs before they are assigned irrevocably to machines. For m identical machines, we show an upper bound of Hm-1+1 for a buffer of size m-1. A competitive ratio below Hm is not possible with any fixed buffer size, and it requires a buffer of size Ω(m/logm) to get a ratio of O(logm). 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 competitive ratio below 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 that 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.
Starting Page	1230
Ending Page	1250
Page Count	21
File Format	PDF
ISSN	08954801
DOI	10.1137/100794006
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	25
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-08-16
Access Restriction	Subscribed
Subject Keyword	Online algorithms scheduling competitive Scheduling theory, deterministic analysis Analysis of algorithms semionline algorithms max-min allocations
Content Type	Text
Resource Type	Article
Subject	Mathematics

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