An $O(n^2)$ Algorithm for Computing Optimal Continuous Voltage Schedules

Dynamic Voltage Scaling techniques allow the processor to set its speed dynamically in order to reduce energy consumption. In the continuous model, the processor can run at any speed, while in the discrete model, the processor can only run at finite number of speeds given as input. The current best algorithm for computing the optimal schedules for the continuous model runs at $O(n^2\log n)$ time for scheduling $n$ jobs. In this paper, we improve the running time to $O(n^2)$ by speeding up the calculation of s-schedules using a more refined data structure. For the discrete model, we improve the computation of the optimal schedule from the current best $O(dn\log n)$ to $O(n\log \max\{d,n\})$ where $d$ is the number of allowed speeds.