### Abstract

This paper investigates the semi-online version of scheduling problem P∥Cmax on a three-machine system. We assume that all jobs have their processing times between p and rp (p>0,r≥1). We give a comprehensive competitive ratio of LS algorithm which is a piecewise function on r≥1. It shows that LS is an optimal semi-online algorithm for every r∈[1,1.5], [3,2] and [6,+∞). We further present an optimal algorithm for every r∈[2,2.5], and an almost optimal algorithm for every r∈(2.5,3] where the largest gap between its competitive ratio and the lower bound of the problem is at most 0.01417. We also present an improved algorithm with smaller competitive ratio than that of LS for every r∈(3,6).

Original language | English |
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Pages (from-to) | 140-159 |

Number of pages | 20 |

Journal | Discrete Applied Mathematics |

Volume | 150 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Sep 1 2005 |

### Fingerprint

### Keywords

- Analysis of algorithm
- Competitive ratio
- Scheduling
- Semi-online

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Semi-online scheduling jobs with tightly-grouped processing times on three identical machines.** / He, Yong; Dósa, G.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 150, no. 1-3, pp. 140-159. https://doi.org/10.1016/j.dam.2004.12.005

}

TY - JOUR

T1 - Semi-online scheduling jobs with tightly-grouped processing times on three identical machines

AU - He, Yong

AU - Dósa, G.

PY - 2005/9/1

Y1 - 2005/9/1

N2 - This paper investigates the semi-online version of scheduling problem P∥Cmax on a three-machine system. We assume that all jobs have their processing times between p and rp (p>0,r≥1). We give a comprehensive competitive ratio of LS algorithm which is a piecewise function on r≥1. It shows that LS is an optimal semi-online algorithm for every r∈[1,1.5], [3,2] and [6,+∞). We further present an optimal algorithm for every r∈[2,2.5], and an almost optimal algorithm for every r∈(2.5,3] where the largest gap between its competitive ratio and the lower bound of the problem is at most 0.01417. We also present an improved algorithm with smaller competitive ratio than that of LS for every r∈(3,6).

AB - This paper investigates the semi-online version of scheduling problem P∥Cmax on a three-machine system. We assume that all jobs have their processing times between p and rp (p>0,r≥1). We give a comprehensive competitive ratio of LS algorithm which is a piecewise function on r≥1. It shows that LS is an optimal semi-online algorithm for every r∈[1,1.5], [3,2] and [6,+∞). We further present an optimal algorithm for every r∈[2,2.5], and an almost optimal algorithm for every r∈(2.5,3] where the largest gap between its competitive ratio and the lower bound of the problem is at most 0.01417. We also present an improved algorithm with smaller competitive ratio than that of LS for every r∈(3,6).

KW - Analysis of algorithm

KW - Competitive ratio

KW - Scheduling

KW - Semi-online

UR - http://www.scopus.com/inward/record.url?scp=23944465400&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23944465400&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2004.12.005

DO - 10.1016/j.dam.2004.12.005

M3 - Article

AN - SCOPUS:23944465400

VL - 150

SP - 140

EP - 159

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -