Abstract
We consider the problem of scheduling of n independent jobs on m unrelated machines to minimize the max(t 1 , t 2 ,..., t m ), t i being the completion time of machine i. In [1] was suggested a polynomial 2-approximation algorithm for this problem. It was also proved that there can exist no polynomial 1.5-approximation algorithm unless P = NP. Here we improve this earlier performance bound 2 to 2 - 1/m. In [1] is also proved a general rounding theorem, which allows to construct in polynomial time 1-job approximations to the optimum, i.e. schedules with an absolute bound equal to the largest job processing time. We also improve this result and obtain (1—1/m)-job approximation to optimal.
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Shchepin, E.V., Vakhania, N.N. (2000). Task Distributions on Multiprocessor Systems. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds) Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics. TCS 2000. Lecture Notes in Computer Science, vol 1872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44929-9_10
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DOI: https://doi.org/10.1007/3-540-44929-9_10
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