Rearrangeable multirate multicast switching networks are customarily called rearrangeable multirate distributors. It has been known for a long time that rearrangeable multirate distributors with cross‐point complexity O(nlog 2
n) can be constructed, where n is the number of inputs (and outputs) of the switching network. The problem of constructing optimal distributors remains open thus far. This paper gives a general construction of rearrangeable multirate distributors with given depths. One byproduct is a rearrangeable multirate distributor with crosspoint complexity O(nlog n). We also show that this cross‐point complexity is optimal, settling the aforementioned open problem. One of the key ingredients of our new construction is the notion of multirate concentrators. The second ingredient is a multirate version of the Pippenger network. We show how to construct given‐depth multirate concentrators and given‐depth multirate Pippenger networks with small sizes. When the depth is chosen to optimize the size, we obtain the optimal O(nlog n) cross‐point complexity.
