### Abstract

In this paper we consider the problem of semi-online scheduling on two uniform processors, in the case where the total sum of the tasks is known in advance. Tasks arrive one at a time and have to be assigned to one of the two processors before the next one arrives. The assignment cannot be changed later. The objective is the minimization of the makespan. Assume that the speed of the fast processor is s, while the speed of the slow one is normalized to 1. As a function of s, we derive general lower bounds on the competitive ratio achievable with respect to offline optimum, and design on-line algorithms with guaranteed upper bound on their competitive ratio. The algorithms presented for s ≥ sqrt(3) are optimal, as well as for s = 1 and for frac(1 + sqrt(17), 4) ≤ s ≤ frac(1 + sqrt(3), 2).

Original language | English |
---|---|

Pages (from-to) | 211-219 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 393 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Mar 20 2008 |

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### Keywords

- Competitive analysis
- Semi-online scheduling
- Uniform processors

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Theoretical Computer Science*,

*393*(1-3), 211-219. https://doi.org/10.1016/j.tcs.2007.12.005

**Semi-online scheduling on two uniform processors.** / Angelelli, Enrico; Speranza, Maria Grazia; Tuza, Z.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 393, no. 1-3, pp. 211-219. https://doi.org/10.1016/j.tcs.2007.12.005

}

TY - JOUR

T1 - Semi-online scheduling on two uniform processors

AU - Angelelli, Enrico

AU - Speranza, Maria Grazia

AU - Tuza, Z.

PY - 2008/3/20

Y1 - 2008/3/20

N2 - In this paper we consider the problem of semi-online scheduling on two uniform processors, in the case where the total sum of the tasks is known in advance. Tasks arrive one at a time and have to be assigned to one of the two processors before the next one arrives. The assignment cannot be changed later. The objective is the minimization of the makespan. Assume that the speed of the fast processor is s, while the speed of the slow one is normalized to 1. As a function of s, we derive general lower bounds on the competitive ratio achievable with respect to offline optimum, and design on-line algorithms with guaranteed upper bound on their competitive ratio. The algorithms presented for s ≥ sqrt(3) are optimal, as well as for s = 1 and for frac(1 + sqrt(17), 4) ≤ s ≤ frac(1 + sqrt(3), 2).

AB - In this paper we consider the problem of semi-online scheduling on two uniform processors, in the case where the total sum of the tasks is known in advance. Tasks arrive one at a time and have to be assigned to one of the two processors before the next one arrives. The assignment cannot be changed later. The objective is the minimization of the makespan. Assume that the speed of the fast processor is s, while the speed of the slow one is normalized to 1. As a function of s, we derive general lower bounds on the competitive ratio achievable with respect to offline optimum, and design on-line algorithms with guaranteed upper bound on their competitive ratio. The algorithms presented for s ≥ sqrt(3) are optimal, as well as for s = 1 and for frac(1 + sqrt(17), 4) ≤ s ≤ frac(1 + sqrt(3), 2).

KW - Competitive analysis

KW - Semi-online scheduling

KW - Uniform processors

UR - http://www.scopus.com/inward/record.url?scp=39649115197&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649115197&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2007.12.005

DO - 10.1016/j.tcs.2007.12.005

M3 - Article

VL - 393

SP - 211

EP - 219

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-3

ER -