Simulation of large networks on smaller networks

Parallel algorithms are normally designed for execution on networks of N processors, with N depending on the size of the problem to be solved. In practice there will be a varying problem size but a fixed network size. In Fishburn and Finkel (IEEE Trans. Comput. 31 (1982), 288-295), the notion of network emulation was proposed, to obtain a structure preserving simulation of large networks on smaller networks. We present a detailed analysis of the possible emulations for some important classes of networks, namely: the shuffle-exchange network, the cube network, the ring network, and the 2-dimensional grid. We also study the possibility of cross-emulations, and characterize the networks that can be emulated at all on a given network using some class of emulation functions.