Abstract
We present deterministic upper and lower bounds on the slowdown required to simulate an (n,m)-PRAM on a variety of networks. The upper bounds are based on a novel scheme that exploits the splitting and combining of messages. Such a scheme can be implemented on an n-node d-dimensional mesh, with d constant, and on an n-leaf pruned butterfly, attaining the best worst-case slowdowns to date for such interconnections. Moreover, the one for the pruned butterfly is the first PRAM simulation scheme on an area-universal network. Finally, under the standard point-to-point assumption, we prove a bandwidth-based lower bound on the slowdown of any deterministic PRAM simulation on an arbitrary network, formulated in terms of its decomposition tree.
This research was supported, in part, by the ESPRIT III Basic Research Programme of the EC under contract No. 9072 (project GEPPCOM).
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© 1995 Springer-Verlag Berlin Heidelberg
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Herley, K.T., Pietracaprina, A., Pucci, G. (1995). Implementing shared memory on multi-dimensional meshes and on the fat-tree. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_134
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DOI: https://doi.org/10.1007/3-540-60313-1_134
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