On-line machine covering

Yossi Azar, Leah Epstein

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


We consider the problem of scheduling a sequence of jobs to m parallel machines as to maximize the minimum load over the machines. This situation corresponds to a case that a system which consists of the m machines is alive (i.e. productive) only when all the machines are alive, and the system should be maintained alive as long as possible. It is well known that any on-llne deterministic algorithm for identical machines has a competitive ratio of at least m and that greedy is an m competitive algorithm. In contrast we design an on-line randomized algorithm which is Ö(√M) competitive and a matching lower bound of Ω(√M) for any online randomized algorithm. In the case where the jobs are polynomially related we design an optimal O(log m) competitive randomized algorithm and a matching tight lower bound for any on-line randomized algorithm. In fact, if F is the ratio between the largest job and the smallest job then our randomized algorithm is O(log F) competitive. A sub-problem that we solve which is interesting by its own is the problem where the value of the optimal algorithm is known in advance. Here we show a deterministic (constant) 2-1/m competitive algorithm. We also show that our algorithm is optimal for two, three and four machines and that no on-fine deterministic algorithm can achieve a better competitive ratio than 1.75 for m ≥ 4 machines. For related machines we show that there is no on-line algorithm, whose competitive ratio is a function of the number of machines. However, for the case where the value of the optimal assignment is known in advance, and for the case where jobs arrive in non increasing order, we show that the exact competitive ratio is m. We show a constant 2 competitive algorithm for the intersection of the above two cases, i.e. the value of the optimal assignment is known in advance and the jobs arrive in non increasing order.

Original languageEnglish
Title of host publicationAlgorithms - ESA 1997 - 5th Annual European Symposium, Proceedings
EditorsRainer Burkard, Gerhard Woeginger
PublisherSpringer Verlag
Number of pages14
ISBN (Print)3540633979, 9783540633976
StatePublished - 1997
Externally publishedYes
Event5th Annual European Symposium on Algorithms, ESA 1997 - Graz, Austria
Duration: 15 Sep 199717 Sep 1997

Publication series

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


Conference5th Annual European Symposium on Algorithms, ESA 1997

Bibliographical note

Publisher Copyright:
© 1997, Springer Verlag, All Rights Reserved.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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