Abstract
Multicast transmissions in coded wireless packet networks can be affected by uncertain factors such as the distance between nodes. We develop a robust optimization method to minimize the energy consumption of such multicasts. We therefore consider the distances to belong to closed convex uncertainty sets. As solution, we select the optimum in the worst case over these uncertainty sets. We prove that the complexity of obtaining this robust solution is similar to that of determining a solution of the problem without uncertainty. Numerical results show that the proposed solution significantly reduces the energy consumption of a multicast connection and that it can be obtained quickly enough for practical applications. Compared with the optimal solution of the deterministic problem, the robust results only exhibit a small performance loss, even if the size of the uncertainty set is notably large.
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Data Availability
In accordance with the journal’s policy on data sharing, the data supporting the findings of this study are available upon reasonable request. Researchers interested in accessing the data may contact Mohammad Ali Raayatpanah at raayatpanah@khu.ac.ir to inquire about the availability and access to the relevant datasets.
Notes
There were very few outliers with runtimes of about 1 min in our experiment, which we attribute to the laptop switching to sleep mode and waking up for some reason. The 97.5 percentiles should be very close to the actual maximum, so we present them instead.
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We acknowledge support from the National Natural Science Foundation of China under Grants 61673359 and 61672204 and the Major Science and Technology Project of Anhui Province 17030901026. Prof. Weise acknowledges funding from the National Natural Science Foundation of China under grant 61673359, the Hefei Specially Recruited Foreign Expert program, and the Hefei Foreign Expert Office program.
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Raayatpanah, M.A., Weise, T., Wu, J. et al. Robust optimization for minimizing energy consumption of multicast transmissions in coded wireless packet networks under distance uncertainty. J Comb Optim 46, 4 (2023). https://doi.org/10.1007/s10878-023-01065-y
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DOI: https://doi.org/10.1007/s10878-023-01065-y