Abstract
We investigate the communication capacity and optimal data transmission schedules for processor networks connected by communication links, for example Transputer clusters. Each link allows the two processors at its endpoints to exchange data with a given fixed transmission rate τ d. The communication itself is done in a blocking mode, that means the two processors have to synchronize before starting to exchange data and at any time each processor cannot communicate with more than one other processor.
Our efficiency analysis will be more realistic by also taking into account the setup time for a communication, which will be assumed to be a fixed constant τ s> 0. Thus, a large amount of data can be sent from one processor to a neighbour faster by a single long communication step than by a bunch of small data exchange steps: sending p data units in one step takes time τ s + p · τ d. However, there is a tradeoff since the receiver has to wait until it has received the complete set of data before it can forward pieces to other processors.
The following prototype task called scattering will be considered: At the beginning one processor called the source possesses a set of unit size data packets, one for each processor in the network. The goal is to distribute the packets in minimal time to all recipients.
Our results concerning the complexity of this problem in arbitrary processor networks are as follows: For the general case, we give lower bounds on the minimal schedule length and show that to determine the length precisely is NP-complete. Special classes of simple strategies are investigated in more detail. For certain networks they turn out to yield optimal schedules.
Finally, we investigate optimal schedules that can be computed efficiently and good approximation algorithms for specific regular networks like hypercubes and multidimensional grids.
supported by DFG Research Grant Re 672-2
Preview
Unable to display preview. Download preview PDF.
References
S. N. Bhatt, G. Bilardi, G. Pucci, A. Ranade, A. L. Rosenberg and E. J. Schwabe, On Bufferless Routing of Variable Length Messages in Leveled Networks, 1st European Symp. Algorithms, 1993.
S. N. Bhatt, G. Pucci, A. Ranade and A. L. Rosenberg, Scattering and Gathering Messages in Networks of Processors, IEEE Trans. Computers 42, 1993, 938–949.
J.-C. Bermond, P. Hell, A. Liestman, and J. Peters, Broadcasting in Bounded Degree Graphs, SIAM J. Disc. Math. 5, 1992, 10–24.
P. Fraigniaud, S. Miguet and Y. Robert, Complexity of Scattering on a Ring of Processors, Parallel Computing 13, 1990, 377–383.
S. Hedetniemi, S. Hedetniemi, and A. Liestman, A Survey of Gossiping and Broadcasting in Communication Networks, Networks 18, 1988, 319–349.
J. Hromkovič, C.-D. Jeschke, and B. Monien, Optimal Algorithms for Dissemination of Information in Some Interconnection Networks, Proc. 15th MFCS, 1990, 337–346.
A. Jakoby, Optimal Data Distribution in Blocking Networks, Technical Report Universität Lübeck, in preparation.
S. L. Johnsson and C.-T. Ho, Optimal Broadcasting and Personalized Communication in Hypercubes, IEEE Trans. Computers 38, 1989, 1249–1268.
H. Jung, L. Kirousis, P. Spirakis, Lower Bounds and Efficient Algorithms for Multiprocessor Scheduling of DAGs with Communication Delays, Proc. 1st SPAA, 1989, 254–264.
A. Jakoby, R. Reischuk, The Complexity of Scheduling Problems with Communication Delays for Trees, Proc. 3rd SWAT, 1992, 165–177.
A. Jakoby, R. Reischuk, C. Schindelhauer, The Complexity of Broadcasting in Planar and Decomposable Graphs, Proc. 14th International Workshop on Graph-Theoretic Concepts in Computer Science, Herrsching, June 1994.
A. Liestman and J. Peters, Broadcast Networks of Bounded Degree, SIAM J. Disc. Math. 4, 1988, 531–540.
T. Ottmann and P. Widmayer, Algorithmen und Datenstrukturen, BI Wissenschaftsverlag, 1993.
C. Papadimitriou and M. Yannakakis, Towards an Architecture-Independent Analysis of Parallel Algorithms, Proc. 20th STOC, 1988, 510–513, see also SIAM J. Comput. 19, 1990, 322–328.
P. Slater, E. Cockayne, and S. Hedetniemi, Information Dissemination in Trees, SIAM J. Comput. 10, 1981, 692–701.
Y. Saad and M. H. Schultz, Data Communication in Parallel Architectures, Parallel Computing 11, 1989, 131–150.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jakoby, A., Reischuk, R. (1995). Data transmission in processor networks. In: Hélary, JM., Raynal, M. (eds) Distributed Algorithms. WDAG 1995. Lecture Notes in Computer Science, vol 972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022144
Download citation
DOI: https://doi.org/10.1007/BFb0022144
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60274-3
Online ISBN: 978-3-540-44783-2
eBook Packages: Springer Book Archive