Scheduling Under Power and Energy Constraints

TL;DR

This paper investigates scheduling problems under power, energy, and makespan constraints, revealing NP-hardness in several cases and providing algorithms for optimal and approximate solutions.

Contribution

It characterizes the computational complexity of scheduling under various resource constraints and offers algorithms for both divisible and non-divisible jobs.

Findings

Minimizing makespan with power constraints is NP-hard.

Scheduling to minimize energy under power constraints is NP-hard.

Polynomial-time solutions exist for divisible jobs with energy and makespan constraints.

Abstract

Given a system model where machines have distinct speeds and power ratings but are otherwise compatible, we consider various problems of scheduling under resource constraints on the system which place the restriction that not all machines can be run at once. These can be power, energy, or makespan constraints on the system. Given such constraints, there are problems with divisible as well as non-divisible jobs. In the setting where there is a constraint on power, we show that the problem of minimizing makespan for a set of divisible jobs is NP-hard by reduction to the knapsack problem. We then show that scheduling to minimize energy with power constraints is also NP-hard. We then consider scheduling with energy and makespan constraints with divisible jobs and show that these can be solved in polynomial time, and the problems with non-divisible jobs are NP-hard. We give exact and approximation algorithms for these problems as required.