Asymptotic results for partial concentrators

Various switching network construction advantageously use modules known as partial concentrators. A partial concentrator is an n-input, m-output, single-stage switching device in which each input has access to some but not all of the outputs. A partial concentrator is said to have capacity c, if, for any kor=2. In addition, it is shown that the rate of decrease of the cost ratio with increasing n is logarithmic for M=2, and polynomial for M>or=3.<>