Abstract
The scheduling problem with calibrations was introduced by Bender et al. (SPAA 2013). In sensitive applications, machines need to be periodically calibrated to ensure that they run correctly. Formally, we are given a set of n jobs with release times, deadlines and weights. Calibrating a machine requires a cost and remains calibrated for a period of T time units, after which it must be recalibrated before it can resume running jobs. Moreover, we are given a budget of K calibrations. The objective is to schedule a set of jobs such that the total weight is maximized on m identical machines with at most K calibrations.
In this paper, we present a \((1\mathrm{{/}}3)\)-approximation polynomial time algorithm when jobs have unit processing time. For the arbitrary processing time case, we give a \(((1-\varepsilon )/3)\)-approximation pseudo-polynomial time algorithm and a \(((1-\varepsilon )/18)\)-approximation polynomial time algorithm.
Vincent Chau, Shengzhong Feng and Yong Zhang are supported by Shenzhen research grant (KQJSCX20180330170311901, JCYJ20180305180840138 and GGFW2017073114031767), NSFC (No. 61433012) and Hong Kong GRF 17210017. Minming Li is supported by a grant from Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11268616). Guochuan Zhang is supported by NSFC (No. 11531014).
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Notes
- 1.
A \(\rho \)-approximation algorithm for an optimization problem is a polynomial-time algorithm that for all instances of the problem produces a solution whose value is within a factor of \(\rho \) of the value of an optimal solution. By convention, we have \(\rho >1\) for minimization problems, while \(\rho <1\) for maximization problems.
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Chau, V., Feng, S., Li, M., Wang, Y., Zhang, G., Zhang, Y. (2019). Weighted Throughput Maximization with Calibrations. In: Friggstad, Z., Sack, JR., Salavatipour, M. (eds) Algorithms and Data Structures. WADS 2019. Lecture Notes in Computer Science(), vol 11646. Springer, Cham. https://doi.org/10.1007/978-3-030-24766-9_23
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