An improved upper bound for the subarray partial concentrators

Partial concentrators are used for the assignment of inlets to first-stage switches in the two-stage rearrangeable broadcast networks proposed by Richards and Hwang, who also proposed the subarray method to construct partial concentrators and studied their capacities. An upper bound of the capacity of the subarray partial concentrator was given by Du, Hwang and Richards and conjectured to be the best by Richards and Hwang. In this paper the authors disprove this conjecture by giving a better upper bound.