Efficient communication primitives on hypercubes

We give practical algorithms, complexity analysis and implementation for one-to-all broadcasting, all-to-all personalized communication and matrix transpose (with two-dimensional partitioning of the matrix) on hypercubes. We assume the following communication characteristics: circuit-switched, e-cube routing and one-port communication model. For one-to-all broadcasting, we give an algorithm that combines the well-known recursive doubling algorithm[1] and the algorithm based on edgedisjoint spanning trees[2]. The measured times of the combined algorithm are always superior to those of the edge-disjoint spanning tree algorithm and outperform the recursive doubling algorithm. For all-to-all personalized communication we propose a hybrid algorithm that combines the well-known recursive doubling algorithm[3,4] and the recently proposed direct-route algorithm[5,6] Our hybrid algorithm balances between data transfer time and start-up time of these two algorithms, and its communication complexity is estimated to be better than the two previous algorithms for a range of machine parameters. For matrix transpose with two-dimensional partitioning of the matrix, we relate a two-phase algorithm to the previous result in Reference 7. The algorithm is predicted to be better than the recursive transpose algorithm[8] by n nearest-neighbor communications[4]. It takes advantage of circuit-switched routing and is congestion-free within each phase. We also suggest a way of storing the matrix such that the transpose operation can be realized in one phase without congestion.