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Efficient Mappings of Pyramid Networks
October 1994 (vol. 5 no. 10)
pp. 1009-1017

We consider primarily the simulation of large networks by smaller ones-an importantconsideration, because interconnection networks are typically of a fixed size, and yetapplications may employ networks of a larger size. Current research (Dingle andSudborough, 1993) describes methods to simulate common data structures and networkarchitectures on the pyramid. However, these simulations assume that the pyramid growswith the size of the network or data structure. Because unbounded growth is notfeasible, we address the issue of mapping several points of the guest data structure ornetwork to a single host processor. We determine how a small pyramid may efficientlysimulate the computation of a larger pyramid as well as that of tree networks.

[1] S. K. Bhaskar, A. Rosenfeld and A. Y. Wu, "Simulation of large networks of processors by smaller ones," in L. Uhr, K. Preston, S. Levialdi, and M. Duff, Eds.,Evaluation of Multicomputers for Image Processing. New York: Academic, 1986, pp. 77-89.
[2] A. Dingle and H. Sudborough, "Simulation of binary trees andX- trees on pyramid networks,"J. Parallel Distrib. Computing. vol. 19, pp. 119-124, 1993.
[3] C. Dyer, "Pyramid algorithms and machines," in K. Preston, Jr., L. Uhr, Eds.,Multicomputers and Image Processing: Algorithms and Programs. New York: Academic, 1982, pp. 409-420.
[4] R. Miller and Q. Stout, "Mesh computer algorithms for computational geometry,"IEEE Trans. Comput., vol. C-38, pp. 321-340, 1989.
[5] R. Miller and Q.F. Stout, "Pyramid Computer Algorithms for Determining Geometric Properties of Images,"Proc. Symp. Computational Geometry, ACM, New York, 1985, pp. 263-269.
[6] R. Miller and Q. F. Stout, "Data movement techniques for the pyramid computer,"SIAM J. Comput., vol. 16, pp. 38-60, 1987.
[7] B. Monien, "Simulating arbitrary binary trees on X-trees,"Proc. 1991 ACM Symp. Parallel Algorithms Architectures, 1991, pp. 217-222.
[8] Q. Stout, "Drawing straight lines with a pyramid cellular automaton,"Inform. Processing Lett., vol. 15, pp. 233-237, 1982.
[9] Q. F. Stout, "Hypercubes and pyramids," inPyramidal Systems for Computer Vision, V. Cantoni and S. Levialdi, Eds. Berlin: Springer, 1986.
[10] Q. Stout, "An algorithmic comparison of meshes and pyramids," in L. Uhr, K. Preston, S. Levialdi, and M. Duff, Eds.,Evaluation of Multicomputers for Image Processing. London: Academic, 1986, pp. 107-121.
[11] S. L. Tanimoto, "Architectural issues for intermediate-level vision," inIntermediate-Level Image Processing, M. J. B. Duff, Ed. New York: Academic, 1986, ch. 1, pp. 3-17.
[12] L. Uhr, "Layered 'Recognition Cone' networks that preprocess, classify, and describe,"IEEE Trans. Comput., vol. C-21, pp. 758-768, 1972.

Index Terms:
Index Termsdata structures; graph theory; resource allocation; multiprocessor interconnectionnetworks; trees (mathematics); optimisation; pyramid network mapping; large networksimulation; small networks; interconnection networks; data structures; networkarchitectures; unbounded growth; single host processor; tree networks; graphembeddings; parallel networks; multiprocessors; communication cost; load balancing;simulation modelling
A. Dingle, I.H. Sudborough, "Efficient Mappings of Pyramid Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 10, pp. 1009-1017, Oct. 1994, doi:10.1109/71.313118
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