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An Adversarial Model for Scheduling with Testing

journal contribution
posted on 03.08.2020, 16:40 by Christoph Dürr, Thomas Erlebach, Nicole Megow, Julie Meißner
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 p¯j (which is the time taken to execute the job if it is not tested) to any value between 0 and 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.

Funding

This research was carried out in the framework of MATHEON supported by Einstein Foundation Berlin, the German Science Foundation (DFG) under contract ME 3825/1 and Bayerisch-Französisches Hochschulzentrum (BFHZ). Further support was provided by EPSRC Grant EP/S033483/1 and the ANR Grant ANR-18-CE25-0008.

History

Citation

Algorithmica (2020). https://doi.org/10.1007/s00453-020-00742-2

Author affiliation

School of Informatics

Version

AM (Accepted Manuscript)

Published in

Algorithmica

Volume

94

Publisher

Springer Science and Business Media LLC

issn

0178-4617

eissn

1432-0541

Acceptance date

22/06/2020

Copyright date

2020

Available date

10/07/2021

Notes

A preliminary version of this paper appeared in The 9th Innovations in Theoretical Computer Science Conference (ITCS), January 2018 [16].https://doi.org/10.4230/LIPIcs.ITCS.2018.30

Language

en

Publisher version

https://link.springer.com/article/10.1007/s00453-020-00742-2

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