Competitive analysis

Epistemology

Operating system

Unit of time

Algorithm

Physics

Mathematical optimization

Randomized algorithm

Mathematical analysis

Philosophy

Online algorithm

Scheduling (production processes)

Theory of computation

Mathematics

Computer science

Job shop scheduling

Quantum mechanics

Schedule

A priori and a posteriori

Upper and lower bounds

Algorithmica

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.

An Adversarial Model for Scheduling with Testing