Abstract
We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines.
We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions.
Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.
This work is supported by the German Research Foundation (DFG) under project ME 3825/1 and within project A07 of CRC TRR 154. It is partially funded in the framework of Matheon supported by the Einstein Foundation Berlin and by the Alexander von Humboldt Foundation. A version with proofs and illustrations is available on arXiv.
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We thank the anonymous reviewers for their helpful comments.
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Abed, F. et al. (2017). Scheduling Maintenance Jobs in Networks. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_3
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