We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed scalable processors in a fully heterogeneous setting. For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.
@cite_5 studied the min-power routing problem and for uniform demands, i.e. for the case where all the demands have the same value, they proposed a @math -approximation algorithm, where @math , with @math . For non-uniform demands, they proposed a @math -approximation algorithm, where @math is the maximum value of the demands.
@cite_5
2010781926
We study network optimization that considers power minimization as an objective. Studies have shown that mechanisms such as speed scaling can significantly reduce the power consumption of telecommunication networks by matching the consumption of each network element to the amount of processing required for its carried traffic. Most existing research on speed scaling focuses on a single network element in isolation. We aim for a network-wide optimization. Specifically, we study a routing problem with the objective of provisioning guaranteed speed bandwidth for a given demand matrix while minimizing power consumption. Optimizing the routes critically relies on the characteristic of the speed-power curve f(s), which is how power is consumed as a function of the processing speed s. If f is superadditive, we show that there is no bounded approximation in general for integral routing, i.e., each traffic demand follows a single path. This contrasts with the well-known logarithmic approximation for subadditive functions. However, for common speed-power curves such as polynomials f(s) = μsα, we are able to show a constant approximation via a simple scheme of randomized rounding. We also generalize this rounding approach to handle the case in which a nonzero startup cost σ appears in the speed-power curve, i.e., f(s) = σ + μsα, if s >; 0; 0, if s = 0. We present an O((σ μ)1 α)-approximation, and we discuss why coming up with an approximation ratio independent of the startup cost may be hard. Finally, we provide simulation results to validate our algorithmic approaches.