Data transmission in processor networks
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 τd. 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 τs> 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 τs + p · τd. 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.
Unable to display preview. Download preview PDF.
- [BBP93]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.Google Scholar
- [HHL88]S. Hedetniemi, S. Hedetniemi, and A. Liestman, A Survey of Gossiping and Broadcasting in Communication Networks, Networks 18, 1988, 319–349.Google Scholar
- [HJM90]J. Hromkovič, C.-D. Jeschke, and B. Monien, Optimal Algorithms for Dissemination of Information in Some Interconnection Networks, Proc. 15th MFCS, 1990, 337–346.Google Scholar
- [J95]A. Jakoby, Optimal Data Distribution in Blocking Networks, Technical Report Universität Lübeck, in preparation.Google Scholar
- [JKS89]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.Google Scholar
- [JR92]A. Jakoby, R. Reischuk, The Complexity of Scheduling Problems with Communication Delays for Trees, Proc. 3rd SWAT, 1992, 165–177.Google Scholar
- [JRS94]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.Google Scholar
- [OW93]T. Ottmann and P. Widmayer, Algorithmen und Datenstrukturen, BI Wissenschaftsverlag, 1993.Google Scholar
- [PY88]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.Google Scholar