Optimizing task layout on the Blue Gene/L supercomputer

A general method for optimizing problem layout on the Blue Gene®/L (BG/L) supercomputer is described. The method takes as input the communication matrix of an arbitrary problem as an array with entries C(i, j), which represents the data communicated from domain i to domain j. Given C(i, j), we implement a heuristic map that attempts to sequentially map a domain and its communication neighbors either to the same BG/L node or to near-neighbor nodes on the BG/L torus, while keeping the number of domains mapped to a BG/L node constant. We then generate a Markov chain of maps using Monte Carlo simulation with free energy F = ∑i,jC(i, j)H(i, j), where H(i, j) is the smallest number of hops on the BG/L torus between domain i and domain j. For two large parallel applications, SAGE and UMT2000, the method was tested against the default Message Passing Interface rank order layout on up to 2,048 BG/L nodes. It produced maps that improved communication efficiency by up to 45%.