The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI

It is shown that the binary de Bruijn multiprocessor network (BDM) can solve a wide variety of classes of problems. The BDM admits an N -node linear array, an N-node ring, (N-1)-node complete binary trees, ((3N/4)-2)-node tree machines, and an N-node one-step shuffle-exchange network, where N (=2 ^k, k an integer) is the total number of nodes. The de Bruijn multiprocessor networks are proved to be fault-tolerant as well as extensible. A tight lower bound of the VLSI layout area of the BDM is derived; a procedure for an area-optimal VLSI layout is also described. It is demonstrated that the BDM is more versatile than the shuffle-exchange and the cube-connected cycles. Recent work has classified sorting architectures into (1) sequential input/sequential output, (2) parallel input/sequential output, (3) parallel input/parallel output, (4) sequential input/parallel output, and (5) hybrid input/hybrid output. It is demonstrated that the de Bruijn multiprocessor networks can sort data items in all of the abovementioned categories. No other network which can sort data items in all the categories is known