## Abstract

We study the problem of on-line 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 with competitive ratio (4 - s)(1 + s)/4 ≤ 1.56250. We analyse other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.52778 for any s. These algorithms are barely random, i.e. they use only a constant number of random bits. 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 best possible even among randomized preemptive algorithms.

Original language | English |
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Pages (from-to) | 71-92 |

Number of pages | 22 |

Journal | Journal of Scheduling |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |

## Keywords

- Analysis of algorithms
- Competitive ratio
- On-line algorithms
- Scheduling

## ASJC Scopus subject areas

- Software
- Engineering (all)
- Management Science and Operations Research
- Artificial Intelligence