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Abstract

All of the theoretical speed scaling research to date has assumed that the power function, which expresses the power consumption $P$ as a function of the processor speed $s$, is of the form $P=s^\alpha$, where $\alpha > 1$ is some constant. Motivated in part by technological advances, we initiate a study of speed scaling with arbitrary power functions. We consider the problem of minimizing the total flow plus energy. Our main result is a $(3+\epsilon)$-competitive algorithm for this problem, that holds for essentially any power function. We also give a $(2+\epsilon)$-competitive algorithm for the objective of fractional weighted flow plus energy. Even for power functions of the form $s^\alpha$, it was not previously known how to obtain competitiveness independent of $\alpha$ for these problems. We also introduce a model of allowable speeds that generalizes all known models in the literature.