On-line scheduling with precedence constraints

Yossi Azar, Leah Epstein

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


We consider the on-line problem of scheduling jobs with precedence constraints on m machines. We concentrate in two models, the model of uniformly related machines and the model of restricted assignment. For the related machines model, we show a lower bound of Ω (√ m) for deterministic and randomized on-line algorithms, with or without preemptions even for jobs of known durations. This matches the deterministic upper bound of O(√ m) given by Jaffe for task sys-tems. The lower bound should be contrasted with the known bounds for jobs without precedence constraints. Specifically, without precedence constraints, if we allow preemptions then the competitive ratio becomes θ(logm), and if the durations of the jobs are known then there are O(1) competitive (preemptive and non-preemptive) algorithms. We also consider the restricted assignment model. For the model with consistent precedence constraints, we give a (randomized) lower bound of Ω (logm) with or without preemptions. We show that the (deterministic) greedy algorithm (no preemptions used), is optimal for this model i.e. O(logm) competitive. However, for general precedence constraints, we show a lower bound of m which is easily matched by a greedy algorithm.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
EditorsMagnús M. Halldórsson
PublisherSpringer Verlag
Number of pages11
ISBN (Print)3540676902, 9783540676904
StatePublished - 2000
Externally publishedYes
Event7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway
Duration: 5 Jul 20007 Jul 2000

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


Conference7th Scandinavian Workshop on Algorithm Theory, SWAT 2000

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'On-line scheduling with precedence constraints'. Together they form a unique fingerprint.

Cite this