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Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings

Authors Christoph Damerius, Peter Kling , Minming Li, Chenyang Xu, Ruilong Zhang

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Author Details

Christoph Damerius
  • Department of Informatics, Universität Hamburg, Germany
Peter Kling
  • Department of Informatics, Universität Hamburg, Germany
Minming Li
  • Department of Computer Science, City University of Hong Kong, China
Chenyang Xu
  • Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, China
Ruilong Zhang
  • Department of Computer Science and Engineering, University at Buffalo, NY, USA

Acknowledgements

We thank the anonymous reviewers for their many insightful comments and suggestions. Chenyang Xu was supported in part by Science and Technology Innovation 2030 –"The Next Generation of Artificial Intelligence" Major Project No.2018AAA0100900, and the Dean’s Fund of Shanghai Key Laboratory of Trustworthy Computing, East China Normal University. Ruilong Zhang was supported by NSF grant CCF-1844890.

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Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang. Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ESA.2023.38

Abstract

Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, [Christoph Dürr et al., 2020] has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a (4+ε)-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a (2+ε)-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time 𝒪(poly(n/ε)). Lastly, we show that our results are essentially optimal by providing matching lower bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • scheduling
  • total completion time
  • makespan
  • LP rounding
  • competitive analysis
  • approximation algorithm
  • NP hardness
  • PTAS

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