Randomized online scheduling on two uniform machines

Leah Epstein, John Noga, Steve Seiden, Jiri Sgall, Gerhard Woeginger

Research output: Contribution to conferencePaperpeer-review

Abstract

We study the problem of online scheduling on two uniform machines with speeds 1 and s≥1. A φ≈1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s≥2, but does help for all s<2. We present a simple memoryless randomized algorithm that is (4-s)(1+s)/4≤1.5625 competitive. We analyze other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.53 for any s. These algorithms are barely random, i.e., they use only a constant number of random bits, and similar methods yield also barely random algorithms for scheduling on two and three identical machines. Finally, we present a 1+s/(s2+s+1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is optimal even among randomized preemptive algorithms.

Original languageEnglish
Pages317-326
Number of pages10
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA
Duration: 17 Jan 199919 Jan 1999

Conference

ConferenceProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms
CityBaltimore, MD, USA
Period17/01/9919/01/99

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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