Efficiency of universal parallel computers
We consider parallel computers (PC's) with fixed communication network with bounded degree. We construct a universal PC with n1+0(1/log log (n)) processors which can simulate each PC with n prodessors with a time loss of 0(log log(n)). This improves a result of  where a time loss of 0(log (n)) was achieved but only using 0(n) processors. Furthermore we prove a time-processor trade-off for a very general type of universal PC's, which includes thatone above. This generalizes a result for a simpler type of simulations presented in , where also all results of this paper are included.
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