Max-min online allocations with a reordering buffer

Leah Epstein, Asaf Levin, Rob Van Stee

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 finite buffer size, and it requires a buffer of size to get a ratio of O(logm). For uniformly related machines, we show that a buffer of size m+1 is sufficient to get an approximation ratio of m, which is best possible for any finite sized buffer. Finally, for the restricted assignment model, we show lower bounds identical to those of uniformly related machines, but using different constructions. In addition, we design an algorithm of approximation ratio O(m) which uses a finite sized buffer. 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 an approximation ratio of m already for identical machines, and it is impossible to obtain an algorithm of finite approximation 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 the greedy algorithm on (a specific set of) related machines, whereas our algorithm for related machines completely ignores the speeds until the end, and then only uses the relative order of the speeds.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Pages336-347
Number of pages12
EditionPART 1
DOIs
StatePublished - 2010
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: 6 Jul 201010 Jul 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6198 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference37th International Colloquium on Automata, Languages and Programming, ICALP 2010
Country/TerritoryFrance
CityBordeaux
Period6/07/1010/07/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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