Load balancing of temporary tasks in the ℓp norm

Yossi Azar*, Amir Epstein, Leah Epstein

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We consider the on-line load balancing problem where there are m identical machines (servers). Jobs arrive at arbitrary times, where each job has a weight and a duration. A job has to be assigned upon its arrival to exactly one of the machines. The duration of each job becomes known only upon its termination (this is called temporary tasks of unknown durations). Once a job has been assigned to a machine it cannot be reassigned to another machine. The goal is to minimize the maximum over time of the sum (over all machines) of the squares of the loads, instead of the traditional maximum load. Minimizing the sum of the squares is equivalent to minimizing the load vector with respect to the ℓ2 norm. We show that for the ℓ2 norm greedy algorithm performs within at most 1.50 of the optimum. We show (an asymptotic) lower bound of 1.33 on the competitive ratio of the greedy algorithm. We also show a lower bound of 1.20 on the competitive ratio of any deterministic algorithm. We extend our techniques and analyze the competitive ratio of greedy with respect to the ℓp norm. We show that the greedy algorithm performs within at most 2 - Ω(1/p) of the optimum. We also show a lower bound of 2 - O(lnp/p) on the competitive ratio of any on-line algorithm.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsKlaus Jansen, Roberto Solis-Oba
PublisherSpringer Verlag
Pages53-66
Number of pages14
ISBN (Electronic)3540210792, 9783540210795
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2909
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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