Online Makespan Scheduling under Scenarios

TL;DR

This paper studies online makespan scheduling with scenarios, analyzing the competitiveness of algorithms, establishing bounds, and connecting the problem to hypergraph coloring to derive theoretical insights.

Contribution

It introduces a scenario-based extension of online makespan scheduling, providing tight bounds and novel constructions, and links the problem to hypergraph coloring for theoretical analysis.

Findings

Established tight bounds for online algorithms under various scenarios.

Developed novel constructions for lower bounds using hypergraph coloring.

Connected scheduling problem analysis to hypergraph coloring techniques.

Abstract

We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so that the maximum makespan under a scenario, i.e., the maximum makespan of any schedule restricted to a scenario, is minimized. For varying values of the number of scenarios and machines, we explore the competitiveness of online algorithms. We prove tight and near-tight bounds, several of which are achieved through novel constructions. In particular, we leverage the interplay between the unit processing time case of our problem and the hypergraph coloring problem both ways: We use hypergraph coloring techniques to steer an adversarial family of instances proving lower bounds, which in turn leads to lower bounds for several variants of online hypergraph coloring.