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).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Collaborative Research Centre 901 - On-The-Fly-Computing. http://sfb901.uni-paderborn.de
Brinkmann, A., Kling, P., auf der Heide, F.M., Nagel, L., Riechers, S., Süß, T.: Scheduling shared continuous resources on many-cores. In: Proceedings of the 26th ACM Symposium on Parallelism inAlgorithms and Architectures (SPAA 2014), pp. 128–137. ACM (2014)
Chung, F., Graham, R., Mao, J., Varghese, G.: Parallelism versus memory allocation in pipelined router forwarding engines. Theory Comput. Syst. 39(6), 829–849 (2006)
de la Vega, W.F., Lueker, G.S.: Bin packing can be solved within 1+epsilon in linear time. Combinatorica 1(4), 349–355 (1981)
Dósa, G., Li, R., Han, X., Tuza, Z.: Tight absolute bound for first fit decreasing bin-packing: FFD(l) \(\le \) 11/9 OPT(L) + 6/9. Theoret. Comput. Sci. 510, 13–61 (2013)
Epstein, L., Levin, A., van Stee, R.: Approximation schemes for packing splittable items with cardinality constraints. Algorithmica 62(1–2), 102–129 (2012)
Epstein, L., van Stee, R.: Approximation schemes for packing splittable items with cardinality constraints. In: Kaklamanis, C., Skutella, M. (eds.) WAOA 2007. LNCS, vol. 4927, pp. 232–245. Springer, Heidelberg (2008)
Epstein, L., van Stee, R.: Improved results for a memory allocation problem. Theory Comput. Syst. 48(1), 79–92 (2011)
Happe, M., auf der Heide, F.M., Kling, P., Platzner, M., Plessl, C.: On-the-fly computing: a novel paradigm for individualized IT services. In: Proceedings of the 16th IEEE International Symposium on Object/Component/Service-Oriented Real-Time Distributed Computing (ISORC 2013), pp. 1–10. IEEE Computer Society (2013)
Karmarkar, N., Karp, R.M.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science (FOCS 1982), pp. 312–320. IEEE Computer Society (1982)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-48749-6_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48748-9
Online ISBN: 978-3-319-48749-6
eBook Packages: Computer ScienceComputer Science (R0)