Real-Time Emulations of Bounded-Degree Networks

In this paper, we survey the state of the art in real-time emulations of various bounded-degree networks | that is, where one bounded-degree network performs an arbitrary computation of some other network with only a constant-factor degradation in both space and time. The results use a variety of techniques, from simple embeddings of one network structure into another to quite complex general emula-tions using redundant computation. We also present new results on the emulation of area-and volume-universal networks and trees of meshes on butterry networks. The results collected here give a complete view of current knowledge of the relative computational strength of many bounded-degree networks that have been considered as candidates for the underlying networks in parallel machines.

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