### Abstract

A set of tasks has to be scheduled on three processors and each task requires that a set of the processors be available for a given processing time. The objective of the problem is to determine a nonpreemptive schedule with minimum makespan. The problem is known to be NP-hard in the strong sense. A normal schedule is such that all tasks requiring the same set of processors are scheduled consecutively. We show that, under a certain (uniform) probability distribution on the problem instances, in more than 95% of the instances the best normal schedule is optimal when the number of tasks grows to infinity. For the hard cases it is shown that the relative error produced by the best normal schedule is bounded by 5/4. This result improves the bound of 4/3 known in the literature and the improved bound is shown to be tight.

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

Pages (from-to) | 67-79 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 164 |

Issue number | 1-3 |

Publication status | Published - Feb 10 1997 |

### Fingerprint

### Keywords

- Approximation algorithms
- Graph theoretical models
- Nonpreemptive scheduling
- Normal schedules
- Probabilistic analysis

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*164*(1-3), 67-79.

**Efficiency and effectiveness of normal schedules on three dedicated processors.** / Dell'Olmo, P.; Speranza, M. G.; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 164, no. 1-3, pp. 67-79.

}

TY - JOUR

T1 - Efficiency and effectiveness of normal schedules on three dedicated processors

AU - Dell'Olmo, P.

AU - Speranza, M. G.

AU - Tuza, Z.

PY - 1997/2/10

Y1 - 1997/2/10

N2 - A set of tasks has to be scheduled on three processors and each task requires that a set of the processors be available for a given processing time. The objective of the problem is to determine a nonpreemptive schedule with minimum makespan. The problem is known to be NP-hard in the strong sense. A normal schedule is such that all tasks requiring the same set of processors are scheduled consecutively. We show that, under a certain (uniform) probability distribution on the problem instances, in more than 95% of the instances the best normal schedule is optimal when the number of tasks grows to infinity. For the hard cases it is shown that the relative error produced by the best normal schedule is bounded by 5/4. This result improves the bound of 4/3 known in the literature and the improved bound is shown to be tight.

AB - A set of tasks has to be scheduled on three processors and each task requires that a set of the processors be available for a given processing time. The objective of the problem is to determine a nonpreemptive schedule with minimum makespan. The problem is known to be NP-hard in the strong sense. A normal schedule is such that all tasks requiring the same set of processors are scheduled consecutively. We show that, under a certain (uniform) probability distribution on the problem instances, in more than 95% of the instances the best normal schedule is optimal when the number of tasks grows to infinity. For the hard cases it is shown that the relative error produced by the best normal schedule is bounded by 5/4. This result improves the bound of 4/3 known in the literature and the improved bound is shown to be tight.

KW - Approximation algorithms

KW - Graph theoretical models

KW - Nonpreemptive scheduling

KW - Normal schedules

KW - Probabilistic analysis

UR - http://www.scopus.com/inward/record.url?scp=0008757653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008757653&partnerID=8YFLogxK

M3 - Article

VL - 164

SP - 67

EP - 79

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -