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Scheduling with Obligatory Tests

Authors Konstantinos Dogeas , Thomas Erlebach , Ya-Chun Liang

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LIPIcs.ESA.2024.48.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Competitive ratio
  • Online algorithm
  • Scheduling with testing
  • Sum of completion times

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Abstract

Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance while the time required to execute the processing part becomes known only upon completion of the test. We use competitive analysis to study algorithms for minimizing the sum of completion times for n given jobs on a single machine. As our main result, we prove using a novel analysis technique that the natural 1-SORT algorithm has competitive ratio at most 1.861. For the special case of uniform test times, we show that a simple threshold-based algorithm has competitive ratio at most 1.585. We also prove a lower bound that shows that no deterministic algorithm can be better than √2-competitive even in the case of uniform test times.

Cite As Get BibTex

Konstantinos Dogeas, Thomas Erlebach, and Ya-Chun Liang. Scheduling with Obligatory Tests. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.48

Author Details

Konstantinos Dogeas
  • Department of Computer Science, Durham University, UK
Thomas Erlebach
  • Department of Computer Science, Durham University, UK
Ya-Chun Liang
  • Data Science Institute, Columbia University, New York, NY, USA
  • Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan

Funding

  • Dogeas, Konstantinos: Funded by EPSRC grant EP/S033483/2.
  • Erlebach, Thomas: Supported by EPSRC grants EP/S033483/2 and EP/T01461X/1.

References

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