In this paper, we study the problem of emulating T G steps of an N G -node guest network, G, on an N H -node host network, H.We call an emulation work-preserving if the time required by the host, T H , is O(T G N G /N H ), because then both the guest and host networks perform the same total work (i.e., processor-time product), ⌰(T G N G ), to within a constant factor.We say that an emulation occurs in real-time if T H ϭ O(T G ), because then the host emulates the guest with constant slowdown.In addition to describing several work-preserving and real-time emulations, we also provide a general model in which lower bounds can be proved.Some of the more interesting and diverse consequences of this work include:(1) a proof that a linear array can emulate a (much larger) butterfly in a work-preserving fashion, but that a butterfly cannot emulate an expander (of any size) in a work-preserving fashion,(2) a proof that a butterfly can emulate a shuffle-exchange network in a real-time work-preserving fashion, and vice versa,(3) a proof that a butterfly can emulate a mesh (or an array of higher, but fixed, dimension) in a real-time work-preserving fashion, even though any O(1)-to-1 embedding of an N-node mesh in an N-node butterfly has dilation ⍀(log N), and (4) simple O(N 2 /log 2 N)-area and O(N 3/ 2 /log 3/2 N)-volume layouts for the N-node shuffle-exchange network.

In this paper, we study the problem of emulating TG steps of an NG-node guest network on an NH-node host network. We call an emulation work-preserving if the time required by the host, TH, is Ο(TGNG/NH) because then both the guest and host networks perform the same total work, Θ(TGNG), to within a constant factor. We say that an emulation is real-time if TH = Ο(TG), because then the host emulates the guest with constant delay. Although many isolated emulation results have been proved for specific networks in the past, and measures such as dilation and congestion were known to be important, the field has lacked a model within which general results and meaningful lower bounds can be proved. We attempt to provide such a model, along with corresponding general techniques and specific results in this paper. Some of the more interesting and diverse consequences of this work include: