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This paper considers classical online scheduling problems on uniform machines. We show the tight competitive ratio of LS for any combinations of speeds of three machines. We prove that LS is optimal when s3 ≥ s2 ≥ s1 = 1 and $${s_3^2\geq s_2^2+s_2s_3+s_2}$$ , where s1, s2, s3 are the speeds of three machines. On the other hand, LS can not be optimal for all combinations of machine speeds,...
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