Efficient communication in the folded Petersen interconnection networks
The folded Petersen network is constructed by iteratively applying the cartesian product operation on the well-known Petersen graph. This topology provides regularity, node- and edge-symmetry, optimal connectivity (and therefore maximal fault-tolerance), logarithmic diameter and modularity. With the same node-degree and connectivity, the n-folded Petersen network, F P n , has smaller diameter with more nodes than the 3n-dimensional binary hypercube Q 3n , and its packing density is higher compared to several other product networks.
In this paper, we consider several fundamental communication problems on the folded Petersen network: sending a message from one node to another (or routing), permutation routing, i.e., every node is source and destination of precisely one message, broadcasting a message from a source to all other nodes (one- to- all broadcasting), sending the same message from every node to all other nodes (multinode-broadcasting or gossiping), personalized communications like scattering (sending from a single node distinct messages to each one of the other nodes) and total exchange (each node sending distinct messages to all other nodes).
All of these communication problems are studied under two assumptions, the single link availability (SLA) in which each node can send or receive messages over a single link at each time step, and the multiple link availability (MLA) in which each node can exchange messages with all of its neighbors at each time step. We derive lower bounds for these problems and design optimal algorithms in terms of both time and the number of message transmissions. The results are based on the construction of optimal height spanning trees in the folded Petersen network F P n .
Keywordsbroadcasting folded Petersen graph gossiping interconnection networks personalized communication routing scattering spanning trees total exchange
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- 1.F.T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays — Trees — Hypercubes. Morgan Kaufmann Publishers, San Mateo, CA, 1992.Google Scholar
- 2.B. Monien and H. Sudborough. Embedding one interconnection network in another. In Computational Graph Theory, pages 257–282, Wien, 1990. Springer Verlag.Google Scholar
- 3.G. Chartrand and R.J. Wilson. The Petersen graph. Graphs and Applications (Eds. F. Harary and J.S. Maybee), pages 69–100, 1985.Google Scholar
- 4.S. Öhring and S.K. Das. The folded Petersen network: A new communication-efficient multiprocessor topology. In Proceedings of the 1993 International Conference on Parallel Processing, Volume I, pages 311–314, Aug. 1993.Google Scholar
- 5.S. Öhring and S.K. Das. Mapping dynamic data and algorithm structures into product networks. In Proc. 4th International Symposium on Algorithms and Computation (ISAAC'93), Hong Kong, Lecture Notes in Computer Science, vol. 762, pages 147–156, Dec. 15–17 1993.Google Scholar
- 6.S.L. Johnsson. Communication efficient basic linear algebra computations on hypercube architectures. Journal of Parallel and Distributed Computing, 4, 1987.Google Scholar
- 7.D.P. Bertsekas, C. özveren, G.D. Stamoulis, P. Tseng, and J.N. Tsitsiklis. Optimal communication algorithms for hypercubes. Journal of Parallel and Distributed Computing, 11:263–275, 1991.Google Scholar
- 10.P. Fragopoulou and S.G. Akl. Optimal communication algorithms on the star interconnection network. In Proc. of the Fifth IEEE Symposium on Parallel and Distributed Processing, Dallas, TX, pages 702–711, Dec. 1993.Google Scholar
- 11.P. Fraigniaud and E. Lazard. Methods and problems of communication in usual networks. Technical Report Rapport LIP 91-33, Université de Paris-Sud, France, 1991.Google Scholar
- 12.L. Bhuyan and D.P. Agrawal. Generalized hypercubes and hyperbus structures for a computer network. IEEE Transactions on Computers, C-33:323–333, 1984.Google Scholar
- 14.S.K. Das and A.K. Banerjee. Hyper Petersen network: Yet another hypercube-like topology. In Proceedings of the 4th Symposium on the Frontiers of Massively Parallel Computation (Frontiers' 92), pages 270–277, McLean, Virginia, USA, Oct. 1992.Google Scholar
- 15.S.K. Das, S. öhring, and A.K. Banerjee. Embeddings into hyper Petersen networks: Yet another hypercube-like interconnection topology, accepted for publication in Journal of VLSI Design (special Issue on Interconnection Networks), 1994.Google Scholar
- 16.S. öhring and S.K. Das. The folded Petersen cube networks: New competitors for the hypercube. In Proc. of the Fifth IEEE Symposium on Parallel and Distributed Computing, pages 582–589, Dec. 1993.Google Scholar
- 17.A. Youssef. Cartesian product networks. In Procedings of the 1991 International Conference on Parallel Processing, Vol. I, pages 684–685, 1991.Google Scholar
- 18.Jop Sibeyn. personal communication, September 1993.Google Scholar
- 19.S. öhring, D.H. Hohndel, and S.K. Das. Fault tolerant communication algorithms on the folded Petersen networks based on arc-disjoint spanning trees. Technical Report CRPDC-94-4, University of Wuerzburg, University of North Texas, February 1994.Google Scholar