Parallel solutions for preemptive makespan scheduling on two identical machines

TL;DR

This paper explores online preemptive scheduling on two identical machines, demonstrating that parallel solutions improve performance but cannot achieve optimality with a fixed number of solutions, with algorithms reaching optimal competitive ratios.

Contribution

It introduces parallel solution strategies for online preemptive makespan scheduling and analyzes their effectiveness and limitations in different job presentation scenarios.

Findings

Using two solutions improves performance significantly.

Optimal solutions cannot be achieved with any fixed number of parallel solutions.

Algorithms attain the best possible competitive ratios for each case.

Abstract

We consider online preemptive scheduling of jobs arriving one by one, to be assigned to two identical machines, with the goal of makespan minimization. We study the effect of selecting the best solution out of two independent solutions constructed in parallel in an online fashion. Two cases are analyzed, where one case is purely online, and in the other one jobs are presented sorted by non-increasing sizes. We show that using two solutions rather than one improves the performance significantly, but that an optimal solution cannot be obtained for any constant number of solutions constructed in parallel. Our algorithms have the best possible competitive ratios out of algorithms for each one of the classes.