Better permutations for the single-processor scheduling with time restrictions

In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer B ≥ 2 and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following B -constraint. For any real x , no unit time interval [ x , x + 1 ) is allowed to int...

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Bibliographic Details
Published inOptimization letters Vol. 11; no. 4; pp. 715 - 724
Main Authors Zhang, An, Ye, Feilang, Chen, Yong, Chen, Guangting
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017
Subjects
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Single-processor scheduling
Worst-case analysis
Time restrictions
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Summary:In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer B ≥ 2 and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following B -constraint. For any real x , no unit time interval [ x , x + 1 ) is allowed to intersect more than B jobs. We show that there exists a permutation of the jobs which can be processed within a factor of 5 4 of the optimum (plus an additional small constant) when B ≥ 5 and this factor is best possible. When B = 3 , 4 , the corresponding factor equals B B - 1 . Furthermore, we present an asymptotically optimal permutation for B = 2 . The results for B ≥ 4 improve the previous work on this problem.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-016-1038-0