Abstract
Consider a scheduling problem in which a set of jobs with interjob communication, canonically represented by a weighted tree, needs to be scheduled on m parallel processors interconnected by a shared communication channel. In each time step, we may allow any processed job to use a certain capacity of the channel in order to satisfy (parts of) its communication demands to adjacent jobs processed in parallel. The goal is to find a schedule with minimum length in which communication demands of all jobs are satisfied.
We show that this problem is NP-hard in the strong sense even if the number of processors and the maximum degree of the underlying tree is constant. Consequently, we design and analyze simple approximation algorithms with asymptotic approximation ratio 
in case of paths and a ratio of 
in case of arbitrary trees.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901).
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König, J., Mäcker, A., der Heide, F.M.a., Riechers, S. (2016). Scheduling with Interjob Communication on Parallel Processors. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_41
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DOI: https://doi.org/10.1007/978-3-319-48749-6_41
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