Discrete Min-Energy Scheduling on Restricted Parallel Processors

Different from the previous work on energy-efficient algorithms, which focused on assumption that a task can be assigned to any processor, we study the problem of task Scheduling with the objective of Energy Minimization on Restricted Parallel Processors (SEMRPP). Restriction accounts for affinities between tasks and processors, that is, a task has its own eligible processing set of processors. It assumes all tasks have a prescribed deadline on the execution time. We study the processors run at a finite number of distinct speeds, and the processors cannot change its speed during the computation of a task. Our work is motivated by the practical variable voltage processors that they cannot run at arbitrary speed and the task may be failure if the processor adjusts its speed during the computation of the task. We assess the complexity of the problem and present a polynomial time approximation algorithm with a bounded factor related to the adjacent speed ratio.