# An Adversarial Model for Scheduling with Testing

1 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We consider a novel single-machine scheduling problem where the processing time of a job can potentially be reduced (by an \emph{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. 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 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.
Document type :
Conference papers

https://hal.archives-ouvertes.fr/hal-01545658
Contributor : Christoph Dürr <>
Submitted on : Thursday, June 22, 2017 - 10:29:08 PM
Last modification on : Friday, January 8, 2021 - 5:48:02 PM

### Identifiers

• HAL Id : hal-01545658, version 1

### Citation

Christoph Dürr, Thomas Erlebach, Nicole Megow, Meißner Julie. An Adversarial Model for Scheduling with Testing. Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP), Jun 2017, Seeon, Germany. pp.68--70. ⟨hal-01545658⟩

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