An Adversarial Model for Scheduling with Testing

TL;DR

This paper introduces a new adversarial scheduling model with testing, analyzing online algorithms' competitive ratios for minimizing total completion time and makespan under explorable uncertainty.

Contribution

It presents the first bounds on competitive ratios for scheduling with testing, a novel model balancing testing and execution times.

Findings

Established nearly tight bounds for competitive ratios of algorithms.

Provided optimal algorithms for minimizing makespan.

Analyzed differences between total completion time and makespan objectives.

Abstract

We introduce a novel adversarial model for scheduling with explorable uncertainty. In this model, the processing time of a job can potentially be reduced (by an a priori unknown amount) by testing the job. Testing a job $j$ takes one unit of time and may reduce its processing time from the given upper limit $\bar{p}_j$ (which is the time taken to execute the job if it is not tested) to any value between $0$ and $\bar{p}_j$. This setting is motivated e.g. by applications where a code optimizer can be run on a job before executing it. We consider the objective of minimizing the sum of completion times on a single machine. All jobs are available from the start, but the reduction in their processing times as a result of testing is unknown, making this an online problem that is amenable to competitive analysis. The need to balance the time spent on tests and the time spent on job executions adds a novel flavor to the problem. We give the first and nearly tight lower and upper bounds on the competitive ratio for deterministic and randomized algorithms. We also show that minimizing the makespan is a considerably easier problem for which we give optimal deterministic and randomized online algorithms.