O(logN) Depth Routing Structure Based on truncated Concentrators

잘림구조 집중기에 기초한 O(logN) 깊이의 라우팅 구조

One major limitation of the efficiency of parallel computer designs has been the prohibitively high cost of parallel communication between processors and memories. Linear order concentrators can be used to build theoretically optimal interconnection schemes. Current designs call for building superconcentrators from concentrators, then using these to recursively partition the connection streams O(log2N) times to achieve point-to-point routing. Since the superconcentrators each have O(N) hardware complexity but O(log2N) depth, the resulting networks are optimal in hardware, but they are of O(log2N) depth. This pepth is not better than the O(log2N) depth Bitonic sorting networks, which can be implemented on the O(N) shuffle-exchange network with message passing. This paper introduces a new method of constructing networks using linear order concentrators and expanders, which can be used to build interconnection networks with O(log2N) depth as well as O(Nlog2N) hardware cost. (All logarithms are in base 2 throughout paper)