Abstract
We consider a scheduling problem with machine dependent intervals, where each job consists of m fixed intervals, one on each of the m machines. To schedule a job, exactly one of the m intervals needs to be selected, making the corresponding machine busy for the time period equal to the selected interval. The objective is to schedule a maximum number of jobs such that no two selected intervals from the same machine overlap. This problem is NP-hard and admits a deterministic 1 / 2-approximation. The problem remains NP-hard even if all intervals have unit length, and all m intervals of any job have a common intersection. We study this special case and show that it is APX-hard, and design a 501 / 1000-approximation algorithm.
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Acknowledgements
Kateřina Böhmová is a recipient of the Google Europe Fellowship in Optimization Algorithms, and this research is supported in part by this Google Fellowship. The project has been partially supported by the Swiss National Science Foundation (SNF) under the grant number 200021_156620.
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Böhmová, K., Kravina, E., Mihalák, M. (2016). Approximating Interval Selection on Unrelated Machines with Unit-Length Intervals and Cores. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_30
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DOI: https://doi.org/10.1007/978-3-319-45587-7_30
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