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Scheduling with a processing time oracle
- Source :
- Applied Mathematical Modelling, Applied Mathematical Modelling, 2022, 104, pp.701-720. ⟨10.1016/j.apm.2021.12.020⟩
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- International audience; In this paper we study a single machine scheduling problem with the objective of minimizing the sum of completion times. Each of the given jobs is either short or long. However the processing times are initially hidden to the algorithm, but can be tested. This is done by executing a processing time oracle, which reveals the processing time of a given job. Each test occupies a time unit in the schedule, therefore the algorithm must decide for which jobs it will call the processing time oracle. The objective value of the resulting schedule is compared with the objective value of an optimal schedule, which is computed using full information. The resulting competitive ratio measures the price of hidden processing times, and the goal is to design an algorithm with minimal competitive ratio. Two models are studied in this paper. In the non-adaptive model, the algorithm needs to decide beforehand which jobs to test, and which jobs to execute untested. However in the adaptive model, the algorithm can make these decisions adaptively depending on the outcomes of the job tests. In both models we provide optimal polynomial time algorithms following a two-phase strategy, which consist of a first phase where jobs are tested, and a second phase where jobs are executed obliviously. Experiments give strong evidence that optimal algorithms have this structure. Proving this property is left as an open problem
- Subjects :
- FOS: Computer and information sciences
021103 operations research
Scheduling
Processing time oracle
Applied Mathematics
Uncertainty
0211 other engineering and technologies
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Competitive ratio
010201 computation theory & mathematics
Modeling and Simulation
Computer Science - Data Structures and Algorithms
Data Structures and Algorithms (cs.DS)
[MATH]Mathematics [math]
Subjects
Details
- ISSN :
- 0307904X
- Volume :
- 104
- Database :
- OpenAIRE
- Journal :
- Applied Mathematical Modelling
- Accession number :
- edsair.doi.dedup.....f66d064c54501a5243da58f61e210c25