Abstract
Bender et al. (SPAA 2013) proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be often calibrated. Since calibrations have non negligible cost, it is important to study policies minimizing the calibration cost while performing all the necessary tests. We focus on the single-machine setting and we study the complexity status of different variants of the problem. First, we extend the model by considering that the jobs have arbitrary processing times and that the preemption of jobs is allowed. For this case, we propose an optimal polynomial time algorithm. Then, we study the case where there is many types of calibrations with different lengths and costs. We prove that the problem becomes NP-hard for arbitrary processing times even when the preemption of the jobs is allowed. Finally, we focus on the case of unit-time jobs and we show that a more general problem, where the recalibration of the machine is not instantaneous, can be solved in polynomial time.
This work has been supported by the ALGONOW project of the THALES program and the Special Account for Research Grants of National and Kapodistrian University of Athens, by NSFC (Nos. 61433012, U1435215), and by Shenzhen basic research grant JCYJ20160229195940462.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
An edf policy is a schedule in which at any time, the job with the smallest deadline among the available jobs is scheduled first.
References
New integrated stockpile evaluation program to better ensure weapons stockpile safety, security, reliability (2006). http://www.sandia.gov/LabNews/060331.html
Bender, M.A., Bunde, D.P., Leung, V.J., McCauley, S., Phillips, C.A.: Efficient scheduling to minimize calibrations. In: 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013, pp. 280–287. ACM (2013). http://doi.acm.org/10.1145/2486159.2486193
Fineman, J.T., Sheridan, B.: Scheduling non-unit jobs to minimize calibrations. In: Blelloch, G.E., Agrawal, K. (eds.) Proceedings of the 27th ACM on Symposium on Parallelism in Algorithms and Architectures, SPAA 2015, Portland, OR, USA, 13–15 June 2015, pp. 161–170. ACM (2015). http://doi.acm.org/10.1145/2755573.2755605
Graham, R.L., Lawler, E.L., Lenstra, J.K., Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5, 287–326 (1979)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47(4), 617–643 (2000). http://doi.acm.org/10.1145/347476.347479
Lai, T.: Worst-case analysis of greedy algorithms for the unbounded knapsack, subset-sum and partition problems. Oper. Res. Lett. 14(4), 215–220 (1993). http://dx.doi.org/10.1016/0167-6377(93)90072-O
Lueker, G.: Two NP-complete problems in nonnegative integer programming. Report No. 178, Computer Science Laboratory, Princeton University (1975)
Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32(2), 163–200 (2002). http://dx.doi.org/10.1007/s00453-001-0068-9
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Angel, E., Bampis, E., Chau, V., Zissimopoulos, V. (2017). On the Complexity of Minimizing the Total Calibration Cost. In: Xiao, M., Rosamond, F. (eds) Frontiers in Algorithmics. FAW 2017. Lecture Notes in Computer Science(), vol 10336. Springer, Cham. https://doi.org/10.1007/978-3-319-59605-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-59605-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59604-4
Online ISBN: 978-3-319-59605-1
eBook Packages: Computer ScienceComputer Science (R0)