An adaptive global reduction algorithm for wormhole-routed 2D meshes

This paper presents a global reduction algorithm for wormhole-routed 2D meshes. Well-known reduction algorithms that are optimized for short vectors have complexity O(M log N), where N = nn is the number of nodes, and M the vector length. Algorithms suitable for long vectors have complexity O(p N +M). Previously known asymptotically optimal algorithms with complexity O(log N + M) incur inherent network contention among constituent messages. The proposed algorithm adapts to the given vector length, resulting in complexities O(M log N) for short vectors, O(log N + M) for medium-sized vectors, and O(p N + M) for suuciently long vectors. The O(p N + M) version is preferred to the O(log N + M) version for long vectors, due to its small coeecient associated with M; the dominating factor for such vectors. The algorithm is contention-free in a synchronous environment. Under asynchronous execution models, depth contention (contention among message-passing steps) may occur. However, simulation studies show that the eeect of depth contention on the actual performance is negligible.