Class Of Rearrangeable Networks Research Articles

Comment on "A new routing algorithm for a class of rearrangeable networks"

The original paper presents an efficient algorithm for routing an Omega/sup -1//spl times/Omega nonblocking network. This comment presents an extra step required to mute an Omega+Omega network.

Bit-permute multistage interconnection networks

In this paper, we consider a class of log N stage interconnection networks called Bit-Permute Multistage Interconnection Networks (BPMIN's) where the ports of each switch of a stage are different at only one bit position of their labels. We describe the decomposition structure of the BPMIN's and prove that all of the BPMIN's are topologically equivalent and some of them are functionally equivalent. We also identify a class of 2 log N stage rearrangeable networks called symmetric BPMIN's where two log N stage BPMIN's are connected in sequence. The symmetric BPMIN's are either symmetric or asymmetric and regular or irregular in their inter-stage connections and can be reduced into 2 log N-1 stages by combining the two center stages. We show that the symmetric BPMIN's constitute larger class of rearrangeable networks than ever known. We also propose a general routing algorithm for the symmetric BPMIN's by modifying slightly the looping algorithm of the Benes network.

Rearrangeable three-stage interconnection networks and their routing properties

A rearrangeable network is an interconnection network which can achieve all possible permutations of its inputs' connections to its outputs. One class of rearrangeable networks, which have been studied are Clos three-stage networks. Earlier procedures to route such networks rapidly require an excessive amount of hardware, either in the network itself or in the device required to compute the routing. A class of rearrangeable three-stage networks which is both compact and which can be routed quickly is introduced, along with a routing scheme. Switches are added to the network so as to reduce the interdependence between the switch settings, allowing faster routing while only moderately increasing network complexity. A network with O(Nlog/sup 1.5/N) hardware and O(log/sup 1.5/N) depth is derived from O(log/sup 2.5/N) switch setup time. >

On a class of rearrangeable networks

Benes networks are nonblocking rearrangeable networks that can realize arbitrary permutations without conflict. A class of 2 log/sub b/ N stage networks which are equivalent to the Benes networks is introduced. Networks in this class can be either symmetric or asymmetric in their structure, regular or irregular in their interstage connections, and even, 2 log/sub b/ N or 2 log/sub b/ N-1 stages. All networks in this class are nonblocking rearrangeable. A switch labeling scheme is proposed to provide testing of the topological and functional equivalency for this class of networks. This switch labeling scheme can also provide a novel matrix representation for network configuration. This representation introduces a portability concept for the routing scheme on this class of networks. With this representation, a general routing scheme is also developed. This routing scheme can realize arbitrary permutation for the whole class of 2 log/sub b/ N stage networks. >

Rearrangeability of the Five-Stage Shuffle/Exchange Network for N = 8

In this paper we prove the rearrangeubility of a multistage shuffle/exchange network with eight inputs and outputs consisting of five stages. A lower bound of ( 2 log_{2} N - 1 ) stages for rearrangeability of a Shuffle/exchange network with N = 2^{n} inputs and outputs is known; we show its sufficiency for N = 8 . We not only prove the rearrangeability, but also describe an algorithm for routing arbitrary permutations on the network and prove its correctness. In contrast to previous efforts to prove rearrangeability, which rely on topological equivalence to the Benes class of rearrangeable networks, our approach is based on first principles. We also show that two switches in the network are redundant. The results in this paper are useful for establishing an upper bound of ( 3 log_{2} N - 4 ) stages for rearrangeability of a multistage shuffle/exchange network with N \geq 8 , as demonstrated in [12].