Approximation Algorithms for Variable Voltage Processors: Min Energy, Max Throughput and Online Heuristics

Abstract

Dynamic Voltage Scaling techniques allow the processor to set its speed dynamically in order to reduce energy consumption. It was shown that if the processor can run at arbitrary speeds and uses power s ^α when running at speed s, the online heuristic AVR has a competitive ratio (2α)^α/2. In this paper we first study the online heuristics for the discrete model where the processor can only run at d given speeds. We propose a method to transform online heuristic AVR to an online heuristic for the discrete model and prove a competitive ratio $\frac{2^{\alpha-1}(\alpha-1)^{\alpha-1}(\delta^{\alpha}-1)^{\alpha}}{(\delta-1)(\delta^{\alpha}-\delta)^{\alpha-1}}+1$, where δ is the maximum ratio between adjacent non-zero speed levels. We also prove that the analysis holds for a class of heuristics that satisfy certain natural properties. We further study the throughput maximization problem when there is an upper bound for the maximum speed. We propose a greedy algorithm with running time O(n ²logn) and prove that the output schedule is 3-approximation of the throughput and $\frac{(\alpha-1)^{\alpha-1}(3^{\alpha}-1)^{\alpha}}{2\alpha^{\alpha}(3^{\alpha-1}-1)^{\alpha-1}}$-approximation of the energy consumption.

This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 116907].