Abstract
We introduce and analyze a new interconnection topology, called the n-folded Petersen network(F P n ), which is constructed by iteratively applying the cartesian product operation on the well-known Petersen graph itself. The FP n topology provides regularity, node- and edge-symmetry, optimal connectivity (and therefore maximal fault-tolerance), logarithmic diameter, modularity, and simple routing and broadcasting algorithms even in the presence of faults. With the same node-degree and connectivity, F P n has smaller diameter and accommodates more nodes than the 3n-dimensional binary hypercube.
This paper also emphasizes the versatility of FP n as a multiprocessor interconnection topology by providing embeddings of many computationally important structures such as rings, multi-dimensional meshes, hypercubes, complete binary trees, X-trees, tree machines, pyramids and dynamically evolving binary trees.
This work is partially supported by Texas Advanced Research Program Grant under Award No. 003594003.
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References
L. Bhuyan and D.P. Agrawal. Generalized hypercubes and hyperbus structures for a computer network. IEEE Transactions on Computers, C-33, pp. 323–333, 1984.
S.N. Bhatt and Jin-Yi Cai. Take a walk, grow a tree. In Proc. of the 29th Annual Symposium on Foundations of Computer Science, pp. 469–478, Los Alamitos, USA, 1989.
J.C. Bermond and C. Peyrat. de bruijn and kautz networks: a competitor for the hypercube? In Hypercubes and Distributed Computers, pp. 279–293, North-Holland, 1989.
G. Chartrand and R.J. Wilson. The petersen graph. Graphs and Applications (Eds. F. Harary and J.S. Maybee), pp. 69–100, 1985.
N.G. de Bruijn. A combinatorial problem. In Proceedings, volume 49, part 20, pp. 758–764. Akademe Van Wetenschappen, 1946.
S.K. Das and A.K. Banerjee. Hyper petersen network: yet another hypercube-like topology. In Proc. of the 4th Symposium on the Frontiers of Massively Parallel Computation (Frontiers' 92), pp. 270–277, McLean, Virginia, Oct. 1992.
S.K. Das,J. Ghosh, and N. Deo. Stirling networks: a versatile combinatorial topology for multiprocessor systems. Discrete Applied Mathematics, 37/38, special double volume on interconnection networks, pp. 119–146, Jul. 1992.
S.K. Das and S. Öhring. Embeddings of tree-related topologies in hyper Petersen networks. Tech. Rep. CRPDC-92-16, Univ. North Texas, Univ. Würzburg, Sep. 1992.
E. Ganesan and D.K. Pradhan. The hyper-de bruijn multiprocessor networks. In Proc. Conf. on Distributed Computing Systems, pp. 492–499, Arlington, TX, May 1991.
F.T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays — Trees — Hypercubes. Morgan Kaufmann Publishers, San Mateo, CA, 1992.
F.T. Leighton, M. Newmann, A.G. Ranade, and E. Schwabe. Dynamic tree embeddings in butterflies and hypercubes. In Proc. of the 1989 ACM Symposium on Parallel Algorithms and Architectures, pp. 224–234, Santa Fe, NM, Jun. 1989.
B. Monien and H. Sudborough. Embedding one interconnection network in another. In Computational Graph Theory, pp. 257–282, Wien, 1990. Springer Verlag.
S. Öhring and S.K. Das. Dynamic embeddings of trees and quasi-grids into hyper-de bruijn networks,. In Proc. of the 7th International Parallel Processing Symposium, Newport Beach, CA, pp. 519–523, Apr. 1993.
S. Öhring and S.K. Das. The folded Petersen cube networks: new competitors for the hypercube. to appear in Proc. of the Fifth IEEE Symposium on Parallel and Distributed Processing, Dallas, TX, Dec. 1993.
S. Öhring and S.K. Das. The folded Petersen network: a new communication-efficient multiprocessor topology. In Proc. of the 1993 International Conference on Parallel Processing, Volume I, pp. 311–314, St. Charles, IL, Aug. 1993.
S. Öhring and S.K. Das. Folded Petersen Cube Network: New Competitors for the Hypercubes. Tech. Rep. CRPDC-93-8, Univ. Würzburg, Univ. North Texas, Jun. 1993.
S. Öhring and S.K. Das. Mapping dynamic data structures on product networks. Tech. Rep. CRPDC-93-5, Univ. Wüzburg, Univ. North Texas, Mar. 1993.
S. Öhring and S.K. Das. Optimal communication primitives on the folded Petersen networks. Tech. Rep. CRPDC-93-13, Univ. Würzburg, Univ. North Texas, Sep. 1993.
S. Öhring. Dynamic embeddings of trees into de Bruijn graphs. In Proc. Second Joint International Conference on Vector and Parallel Processing, CONPAR 92-VAPPV, Lyon, France, Sep. 1992. LNCS 634, pp. 783–784, 1992.
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Öhring, S.R., Das, S.K. (1994). The folded Petersen network: A new versatile multiprocessor interconnection topology. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_61
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DOI: https://doi.org/10.1007/3-540-57899-4_61
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