Efficient Nonblocking Switching Networks for Interprocessor Communications in Multiprocessor Systems

• Authors: Fong-Chih Shao;A. Yavuz Oruç
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 1995

The performance of a multiprocessor system depends heavily on its ability to provide conflict free paths among its processors. In this paper, we explore the possibility of using a nonblocking network with $O(N \log N)$ edges (crosspoints) to interconnect the processors of an $N$ processor system. We combine Bassalygo and Pinsker's implicit design of strictly nonblocking networks with an explicit construction of expanders to obtain a strictly nonblocking network with $-765.18 N + 352.8 N \log N$ edges and $2+\log (N/5)$ depth. We present an efficient parallel algorithm for routing connection requests on this network and implement it on three parallel processor topologies. The implementation on a parallel processor whose processing elements are interconnected as in the Bassalygo驴Pinsker network requires $O(N\log N)$ processing elements, $O(N\log N)$ interprocessor links and it takes $O(\log N)$ steps to route any single connection request where each step involves a small number ($\approx$72) of bit-level operations. A contracted or folded version of the same implementation reduces the processing element count to $O(N)$ without increasing the link count or the routing time. Finally, we establish that the same algorithm takes $O(\log^3 N)$ steps on a perfect shuffle processor with $O(N)$ processing elements. These results improve the crosspoint, depth and routing time complexities of the previously reported strictly nonblocking networks.Index Terms驴Bassalygo驴Pinsker network, Clos network, Cantor network, extensive graph, expander, parallel routing algorithm, strictly nonblocking network.