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

Yong He, G. Dósa

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 languageEnglish
Pages (from-to)140-159
Number of pages20
JournalDiscrete Applied Mathematics
Volume150
Issue number1-3
DOIs
Publication statusPublished - Sep 1 2005

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Online Scheduling
Competitive Ratio
Scheduling
Optimal Algorithm
Processing
Online Algorithms
Scheduling Problem
Lower bound

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.

In: Discrete Applied Mathematics, Vol. 150, No. 1-3, 01.09.2005, p. 140-159.

Research output: Contribution to journalArticle

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