On synchronous strictly non-blocking concentrators and generalized-concentrators

Abstract

The optimal bound of (n-m+c)c+(m-c) and an Omega (k(n-m+c)c/sup 1/k/) lower bound on the size of synchronous strictly non-blocking c-limited (n,m)-concentrators with depth 1 and depth k respectively are proved. A consequence of the lower-bound result is an Theta (n/sup 1+1/k/) bound on the size of synchronous strictly non-blocking fixed ratio gamma n-limited ( alpha n, beta n)-concentrators ( gamma < beta ) with constant depth k. For synchronous strictly non-blocking (c,r)-limited (n,m)-generalized-concentrators, the optimal size of nc-(/sup m-c///sub r/)(c-r) for depth 1 and a lower bound size-depth tradeoff Omega ((n-/sup m///sub r/+/sup c///sub r/)r/sup k-1/k/c/sup 1/k/) for constant depth k and r=o(c) are also presented.<>