A new algorithm for online uniform-machine scheduling to minimize the makespan

Authors:
T. C. E. Cheng;C. T. Ng;Vladimir Kotov
Affiliations:
Department of Logistics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Department of Logistics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Faculty of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus
Venue:
Information Processing Letters
Year:
2006

Citing 1
Cited 2

An On-Line Algorithm for Some Uniform Processor Scheduling

SIAM Journal on Computing

Competitive ratio of List Scheduling on uniform machines and randomized heuristics

Journal of Scheduling
Online scheduling on three uniform machines

Discrete Applied Mathematics

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Abstract

We consider the online scheduling problem with m - 1, m ≥ 2, uniform machines each with a processing speed of 1, and one machine with a speed of s, 1 ≤ s ≤ 2, to minimize the makespan. The well-known list scheduling (LS) algorithm has a worst-case bound of (3m - 1)/(m + 1) [Y. Cho, S. Sahni, Bounds for list schedules on uniform processors, SIAM J. Comput. 9 (1980) 91-103]. An algorithm with a better competitive ratio was proposed in [R. Li, L. Shi, An on-line algorithm for some uniform processor scheduling, SIAM J. Comput. 27 (1998) 414-422]. It has a worst-case bound of 2.8795 for a big m and s = 2. In this note we present a 2.45-competitive algorithm for m ≥ 4 and any s, 1 ≤ s ≤ 2.