## 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/(s^{2}+s+1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is optimal even among randomized preemptive algorithms.

Original language | English |
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Pages | 317-326 |

Number of pages | 10 |

State | Published - 1999 |

Externally published | Yes |

Event | Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA Duration: 17 Jan 1999 → 19 Jan 1999 |

### Conference

Conference | Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | Baltimore, MD, USA |

Period | 17/01/99 → 19/01/99 |

## ASJC Scopus subject areas

- Software
- Mathematics (all)