Energy-efficient scheduling and routing via randomized rounding

Abstract

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speedscaling 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.

Throughput maximization in multiprocessor speed-scaling

“…They proved that the non-preemptive single-machine case is strongly NP-hard even for laminar instances 3 and they proposed a 2 5α−4 -approximation algorithm. This result has been improved recently in [10] where the authors proposed a 2 α−1 (1 + ε)B α -approximation algorithm, wherẽ B α is the generalized Bell number. For instances in which all the jobs have the same processing volume, Bampis et al [9] gave a 2 α -approximation for the single-machine case.…”

Machine Speed Scaling by Adapting Methods for Convex Optimization with Submodular Constraints

“…This means that the same job, when assigned to different machines, incurs different costs even if it is processed at the same speed. These type of problems are studied by Gupta et al (2010Gupta et al ( , 2012, Bampis et al (2016), Albers et al (2016).…”

Scheduling on Power-Heterogeneous Processors

“…When migrations of jobs are not allowed, the problem is strongly N P-hard even in the special case with homogeneous processors and unit work jobs [2]. Furthermore, there exists a (1 + ) α B α -approximation algorithm, where α is the maximum power exponent and B α is the α-generalized Bell number [6]. When both migrations and preemptions are forbidden, the problem is strongly N P-hard even in the case with a single processor [4].…”

“…However, in order to exploit the opportunities offered by the heterogeneous systems, it is essential to focus on the design of new efficient power-aware algorithms taking into account the heterogeneity of these architectures. In this direction, some recent papers [6,16,17] have studied the impact of the introduction of the heterogeneity on the difficulty of some power-aware scheduling problems. Especially in [16], Gupta et al show that well-known priority scheduling algorithms that are energy-efficient for homogeneous systems become energy inefficient for heterogeneous systems.…”

“…For the case where job migrations are allowed and the heterogeneous power functions are convex, an algorithm has been proposed in [6] that returns a solution within an additive factor of far from the optimal and runs in time polynomial to the size of the instance and to 1/ . This result generalizes the results of [1,3,7,11] from the homogeneous setting to the heterogeneous one.…”