### Abstract

We study a variant of the on-line scheduling problem on two parallel processors. The size of the items is unknown and, as soon as an item is released, it must be immediately assigned to a processor and the assignment cannot be changed later. Optimal algorithms (with respect to competitive ratio) are known for some variants of this problem, where some partial information is given on the instance: the sum of the items is known, or a buffer is available to store a finite number of items. In these cases the best possible competitive ratio of the algorithms is 4/3. In this paper we assume that the sum of items is known in advance (supposed to equal 2) and also that the size of items does not exceed a fixed upper bound γ <1. We provide, for all the possible values of γ, a lower bound for the competitive ratio of any algorithm and propose different algorithms, for different ranges of the upper bound, for which a worst-case analysis is provided. The proposed algorithms are optimal for 1/2 ≤ γ ≤ 3/5, γ = 3/4 and 16/17 ≤ γ <1.

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

Pages (from-to) | 243-262 |

Number of pages | 20 |

Journal | Algorithmica (New York) |

Volume | 37 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2003 |

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### Keywords

- Competitive analysis
- Scheduling
- Semi-on-line
- Two parallel processors

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Applied Mathematics
- Safety, Risk, Reliability and Quality

### Cite this

*Algorithmica (New York)*,

*37*(4), 243-262. https://doi.org/10.1007/s00453-003-1037-2

**Semi-on-line scheduling on two parallel processors with an upper bound on the items.** / Angelelli, Enrico; Speranza, Maria Grazia; Tuza, Z.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 37, no. 4, pp. 243-262. https://doi.org/10.1007/s00453-003-1037-2

}

TY - JOUR

T1 - Semi-on-line scheduling on two parallel processors with an upper bound on the items

AU - Angelelli, Enrico

AU - Speranza, Maria Grazia

AU - Tuza, Z.

PY - 2003/12

Y1 - 2003/12

N2 - We study a variant of the on-line scheduling problem on two parallel processors. The size of the items is unknown and, as soon as an item is released, it must be immediately assigned to a processor and the assignment cannot be changed later. Optimal algorithms (with respect to competitive ratio) are known for some variants of this problem, where some partial information is given on the instance: the sum of the items is known, or a buffer is available to store a finite number of items. In these cases the best possible competitive ratio of the algorithms is 4/3. In this paper we assume that the sum of items is known in advance (supposed to equal 2) and also that the size of items does not exceed a fixed upper bound γ <1. We provide, for all the possible values of γ, a lower bound for the competitive ratio of any algorithm and propose different algorithms, for different ranges of the upper bound, for which a worst-case analysis is provided. The proposed algorithms are optimal for 1/2 ≤ γ ≤ 3/5, γ = 3/4 and 16/17 ≤ γ <1.

AB - We study a variant of the on-line scheduling problem on two parallel processors. The size of the items is unknown and, as soon as an item is released, it must be immediately assigned to a processor and the assignment cannot be changed later. Optimal algorithms (with respect to competitive ratio) are known for some variants of this problem, where some partial information is given on the instance: the sum of the items is known, or a buffer is available to store a finite number of items. In these cases the best possible competitive ratio of the algorithms is 4/3. In this paper we assume that the sum of items is known in advance (supposed to equal 2) and also that the size of items does not exceed a fixed upper bound γ <1. We provide, for all the possible values of γ, a lower bound for the competitive ratio of any algorithm and propose different algorithms, for different ranges of the upper bound, for which a worst-case analysis is provided. The proposed algorithms are optimal for 1/2 ≤ γ ≤ 3/5, γ = 3/4 and 16/17 ≤ γ <1.

KW - Competitive analysis

KW - Scheduling

KW - Semi-on-line

KW - Two parallel processors

UR - http://www.scopus.com/inward/record.url?scp=0344981403&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344981403&partnerID=8YFLogxK

U2 - 10.1007/s00453-003-1037-2

DO - 10.1007/s00453-003-1037-2

M3 - Article

VL - 37

SP - 243

EP - 262

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 4

ER -