Greedy Minimum-Energy Scheduling

TL;DR

This paper presents a greedy scheduling algorithm for energy-efficient job scheduling on multiple processors with power-down features, providing a bounded approximation ratio and analyzing its computational complexity.

Contribution

It generalizes a known greedy algorithm from single to multiple processors, establishing energy cost bounds and analyzing algorithm complexity.

Findings

Energy costs are bounded by 2 times the optimal plus processing volume P.

The algorithm runs in O(nf log d) time, with f being max flow computation time.

The approach extends single-processor greedy strategies to multi-processor scenarios.

Abstract

We consider the problem of energy-efficient scheduling across multiple processors with a power-down mechanism. In this setting a set of $n$ jobs with individual release times, deadlines, and processing volumes must be scheduled across $m$ parallel processors while minimizing the consumed energy. Idle processors can be turned off to save energy, while turning them on requires a fixed amount of energy. For the special case of a single processor, the greedy Left-to-Right algorithm guarantees an approximation factor of $2$. We generalize this simple greedy policy to the case of $m \geq 1$ processors running in parallel and show that the energy costs are still bounded by $2 \text{OPT} + P$, where $\text{OPT}$ is the energy consumed by an optimal solution and $P < \text{OPT}$ is the total processing volume. Our algorithm has a running time of $\mathcal{O}(n f \log d)$, where $d$ is the difference between the latest deadline and the earliest release time, and $f$ is the running time of a maximum flow calculation in a network of $\mathcal{O}(n)$ nodes.