Abstract
This paper presents optimal dynamic embeddings of dynamically growing or shrinking trees and three types of dynamically evolving grids into the de Bruijn graphs, and product networks such as (generalized) hypercube, hyper-de Bruijn, hyper Petersen, folded Petersen and product-shuffle networks.
Our results are important in mapping data and algorithm structures into multiprocessor interconnection networks. Tree embeddings can be used to maintain dynamic data structures such as quad-trees in image processing or data dictionaries, or to efficiently parallelize tree-based computations in divide-and-conquer or branch-and-bound algorithms. Dynamic embeddings of grids are used to parallelize solution methods for partial differential equations, for adaptive mesh refinement or hierarchical domain decomposition in approximation and interpolation of surfaces, image processing, or dynamic programming algorithms.
This work is partially supported by Texas Advanced Research Program Grant under Award No. 003594003.
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E. Ganesan and D.K. Pradhan. The hyper-de bruijn multiprocessor networks. In Proc. 11th Conf. on Distributed Computing Systems, pp. 492–499, Arlington, TX, May 1991.
A.L. Rosenberg. Product-shuffle networks: Towards Reconciling Shuffles and Butterflies. Discrete Applied Mathematics, vol. 37/38, July 1992.
S.K. Das and A.K. Banerjee. Hyper petersen network: Yet another hypercube-like topology. In Proc. 4th Symp. on the Frontiers of Massively Parallel Computation (Frontiers' 92), pp. 270–277, McLean, Virginia, USA, Oct. 1992.
S. öhring and S.K. Das. The Folded Petersen Network: A New Communication-Efficient Multiprocessor Topology. In Proc. 1993 Int. Conf. on Parallel Processing., vol. I, pp. 311–314, Aug. 1993.
F.T. Leighton, M.J. Newman, A.G. Ranade, and E.J. Schwabe. Dynamic Tree Embeddings in Butterflies and Hypercubes. SIAM Journal on Computing, 21(4):639–654, Aug. 1992.
S.K. Das and S. öhring. Embeddings ofTree-Related Topologies in Hyper Petersen Networks. Technical Report CRPDC-92-16, Univ. North Texas, Univ. Wuerzburg, Sep. 1992.
S. öhring. Dynamic Tree Embeddings into de Bruijn Graphs. In Lecture Notes in Computer Science, vol. 634, pp. 783–784. Springer, Sep. 1992.
S. öhring and S.K. Das. Dynamic Embeddings of Trees and Quasi-Grids into Hyper-de Bruijn Networks. In Proc. 7th Int. Parallel Processing Symposium, Newport Beach, CA, pp. 519–523, Apr. 1993.
S. öhring and S.K. Das. The Folded Petersen Network: A New Versatile Multiprocessor Interconnection Topology. to appear in Proc. 1993 Int. Workshop on Graph-Theoretic Concepts in Computer Science (WG'93), June 1993.
S. öhring and S.K. Das. The Folded Petersen Cube Networks: New Competitors for the Hypercube. to appear in Proc. Fifth IEEE Symp. on Par. and Dist. Computing, Dec. 1993.
L. Bhuyan and D.P. Agrawal. Generalized Hypercubes and Hyperbus Structures for a Computer Network. IEEE Transactions on Computers, C-33:323–333, 1984.
G. Chartrand and R.J. Wilson. The Petersen Graph. Graphs and Applications (Eds. F. Harary and J.S. Maybee), pp. 69–100, 1985.
S. öhring and S.K. Das. Mapping Dynamic Data Structures on Product Networks. Technical Report CRPDC-93-5, Univ. Wuerzburg, Univ. North Texas, Mar. 1993.
T.F. Chan and Y. Saad. Multigrid Algorithms on the Hypercube Multiprocessor. In IEEE Transactions on Computers, vol. C-35, No. 11, pp. 969–977, Nov. 1986.
L. S. Barasch, S. Lakshmivarahan, and S.K. Dall. Generalized Gray Codes and Their Properties. In Proc. 3rd Int. Conf. on Supercomputing, vol. III, pp. 331–337, 1988.
S.N. Bhatt, F.R.K. Chung, J.-W. Hong, F.T. Leighton, B. Obreníc, A.L. Rosenberg, and E.J. Schwabe. Optimal Embeddings by Butterfly-Like Networks. COINS Technical Report 90-108, Computer and Information Science Department, University of Massachusetts, 1990.
A.L. Rosenberg. personal communication, May 1992.
D.S. Greenberg, L.S. Heath, and A.L. Rosenberg. Optimal Embeddings of Butterfly-Like Graphs in the Hypercube. Math. Systems Theory, 23:61–77, 1990.
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öhring, S.R., Das, S.K. (1993). Mapping dynamic data and algorithm structures into product networks. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_244
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