Optimal Grain Size Computation for Pipelined Algorithms

. In this paper, we present a method for overlapping communications on parallel computers for pipelined algorithms. We first introduce a general theoretical model which leads to a generic computation scheme for the optimal packet size. Then, we use the OPIUM 3 library, which provides an easy-to-use and efficient way to compute, in the general case, this optimal packet size, on the column LU factorization; the implementation and performance measures are made on an Intel Paragon. Keywords : Communications overlap, pipelined algorithms, optimal packet size computation. 1 Introduction Parallel distributed memory machines improve performances and memory capacity but their use adds an overhead due to the communications. To obtain programs that perform and scale well, this overhead must be hidden. Several solutions exist. The choice of a good data distribution is the first step that can be done to lower the number and the size of communications. Depending of the dependences within the cod..