LIPIcs.ESA.2024.48.pdf
- Filesize: 0.77 MB
- 14 pages
Document
Scheduling with Obligatory Tests
Authors
Konstantinos Dogeas 
,
Thomas Erlebach ,
Ya-Chun Liang
-
Part of:
Volume:
32nd Annual European Symposium on Algorithms (ESA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-23
File
Document Identifiers
Author Details
Cite AsGet 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
https://doi.org/10.4230/LIPIcs.ESA.2024.48
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Design and analysis of algorithms
Keywords
- Competitive ratio
- Online algorithm
- Scheduling with testing
- Sum of completion times
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
- Susanne Albers and Alexander Eckl. Explorable uncertainty in scheduling with non-uniform testing times. In Christos Kaklamanis and Asaf Levin, editors, Approximation and Online Algorithms - 18th International Workshop, WAOA 2020, Virtual Event, September 9-10, 2020, Revised Selected Papers, volume 12806 of Lecture Notes in Computer Science, pages 127-142. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-80879-2_9.
- Susanne Albers and Alexander Eckl. Scheduling with testing on multiple identical parallel machines. In Anna Lubiw and Mohammad R. Salavatipour, editors, Algorithms and Data Structures - 17th International Symposium, WADS 2021, Virtual Event, August 9-11, 2021, Proceedings, volume 12808 of Lecture Notes in Computer Science, pages 29-42. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-83508-8_3.
- Evripidis Bampis, Konstantinos Dogeas, Alexander V. Kononov, Giorgio Lucarelli, and Fanny Pascual. Speed scaling with explorable uncertainty. In Kunal Agrawal and Yossi Azar, editors, SPAA '21: 33rd ACM Symposium on Parallelism in Algorithms and Architectures, Virtual Event, USA, 6-8 July, 2021, pages 83-93. ACM, 2021. URL: https://doi.org/10.1145/3409964.3461812.
- Konstantinos Dogeas, Thomas Erlebach, and Ya-Chun Liang. Scheduling with obligatory tests. CoRR, abs/2406.16734, 2024. URL: https://arxiv.org/abs/2406.16734.
- Christoph Dürr, Thomas Erlebach, Nicole Megow, and Julie Meißner. An adversarial model for scheduling with testing. Algorithmica, 82(12):3630-3675, 2020. URL: https://doi.org/10.1007/s00453-020-00742-2.
- Mingyang Gong, Zhi-Zhong Chen, and Kuniteru Hayashi. Approximation algorithms for multiprocessor scheduling with testing to minimize the total job completion time. Algorithmica, 2023. URL: https://doi.org/10.1007/s00453-023-01198-w.
- Mingyang Gong, Randy Goebel, Guohui Lin, and Eiji Miyano. Improved approximation algorithms for non-preemptive multiprocessor scheduling with testing. J. Comb. Optim., 44(1):877-893, 2022. URL: https://doi.org/10.1007/S10878-022-00865-Y.
- Mingyang Gong and Guohui Lin. Improved approximation algorithms for multiprocessor scheduling with testing. In Jing Chen, Minming Li, and Guochuan Zhang, editors, Frontiers of Algorithmics - International Joint Conference, IJTCS-FAW 2021, Beijing, China, August 16-19, 2021, Proceedings, volume 12874 of Lecture Notes in Computer Science, pages 65-77. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-97099-4_5.
- Retsef Levi, Thomas L. Magnanti, and Yaron Shaposhnik. Scheduling with testing. Management Science, 65(2):776-793, 2019. URL: https://doi.org/10.1287/MNSC.2017.2973.
- Alison Hsiang-Hsuan Liu, Fu-Hong Liu, Prudence W. H. Wong, and Xiao-Ou Zhang. The power of amortization on scheduling with explorable uncertainty. In Jaroslaw Byrka and Andreas Wiese, editors, Approximation and Online Algorithms - 21st International Workshop, WAOA 2023, Amsterdam, The Netherlands, September 7-8, 2023, Proceedings, volume 14297 of Lecture Notes in Computer Science, pages 90-103. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-49815-2_7.
- Rajeev Motwani, Steven J. Phillips, and Eric Torng. Non-clairvoyant scheduling. Theor. Comput. Sci., 130(1):17-47, 1994. URL: https://doi.org/10.1016/0304-3975(94)90151-1.
- Wayne E. Smith. Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3(1-2):59-66, 1956. URL: https://doi.org/10.1002/nav.3800030106.