Abstract
In semi-online scheduling problems, we always assume that some partial additional information is exactly known in advance. This may not be true in some application. This paper considers semi-online problems on identical machines with inexact partial information. Three versions are considered, where we know in advance that the total size of all jobs, the optimal value, and the largest job size are in given intervals, respectively, while their exact values are unknown. We give both lower bounds of the problems and competitive ratios of algorithms as functions of a so-called disturbance parameter r ∈ [1, ∞ ). We establish that for which r the inexact partial information is useful to improve the performance of a semi-online algorithm with respect to its pure online problem. Optimal or near optimal algorithms are then obtained.
Supported by NSFC (10301028, 10271110, 60021201) and TRAPOYT of China.
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References
Azar, Y., Regev, O.: On-line bin-stretching. Theoretical Computer Science 168, 17–41 (2001)
Cheng, T.C.E., Kellerer, H., Kotov, V.: Semi-on-line multiprocessor scheduling with given total processing time, Theoretical Computer Science, Published online doi:10.1016/j.tcs.2004.11.018
Dósa, G., He, Y.: Semi-online agorithms for parallel machine scheduling problems. Computing 72, 355–363 (2004)
Epstein, L.: Bin stretching revisited. Acta Informatica 39, 97–117 (2003)
Faigle, U., Kern, W., Turan, G.: On the performance of online algorithms for partition problems. Acta Cybernetica 9, 107–119 (1989)
Graham, R.L.: Bounds for certain multiprocessor anomalies. Bell Systems Technical Journal 45, 1563–1581 (1966)
He, Y., Dósa, G.: Semi-online scheduling jobs with tightly-grouped processing times on three identical machines. Discrete Applied Mathematics (to appear)
He, Y., Zhang, G.: Semi on-line scheduling on two identical machines. Computing 62, 179–187 (1999)
Kellerer, H., Kotov, V., Speranza, M.G., Tuza, Z.: Semi on-line algorithms for the partition problem. Operations Research Letters 21, 235–242 (1997)
Seiden, S., Sgall, J., Woeginger, G.: Semi-online scheduling with decreasing job sizes. Operations Research Letters 27, 215–227 (2000)
Tan, Z.Y., He, Y.: Semi-on-line problems on two identical machines with combined partial information. Operations Research Letters 30, 408–414 (2002)
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© 2005 Springer-Verlag Berlin Heidelberg
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Tan, Z., He, Y. (2005). Semi-online Problems on Identical Machines with Inexact Partial Information. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_31
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DOI: https://doi.org/10.1007/11533719_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
Online ISBN: 978-3-540-31806-4
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