Throughput Maximization in the Speed-Scaling Setting

TL;DR

This paper addresses throughput maximization in speed-scaling scheduling with energy constraints, proposing algorithms for preemptive and non-preemptive cases, including weighted and unweighted scenarios, with efficiency improvements.

Contribution

It introduces a dynamic programming algorithm for the preemptive case and a strongly polynomial algorithm for the non-preemptive unweighted case, advancing scheduling theory.

Findings

Provides a pseudo-polynomial time algorithm for preemptive scheduling.

Offers a strongly polynomial algorithm for non-preemptive unweighted scheduling.

Adapts algorithms for weighted and non-preemptive scenarios.

Abstract

We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget of energy $E$ and we study the scheduling problem of maximizing the throughput (i.e. the number of jobs which are completed on time). We propose a dynamic programming algorithm that solves the preemptive case of the problem, i.e. when the execution of the jobs may be interrupted and resumed later, in pseudo-polynomial time. Our algorithm can be adapted for solving the weighted version of the problem where every job is associated with a weight $w_j$ and the objective is the maximization of the sum of the weights of the jobs that are completed on time. Moreover, we provide a strongly polynomial time algorithm to solve the non-preemptive unweighed case when the jobs have the same processing requirements. For the weighted case, our algorithm can be adapted for solving the non-preemptive version of the problem in pseudo-polynomial time.