**MapReduce in MPI for Large-Scale Graph Algorithms**

S. J. Plimpton and K. D. Devine, accepted for a special issue of Parallel Computing. To appear in 2011.

We describe a parallel library written with message-passing (MPI) calls that allows algorithms to be expressed in the MapReduce paradigm. This means the calling program does not need to include explicit parallel code, but instead provides ``map'' and ``reduce'' functions that operate independently on elements of a data set distributed across processors. The library performs needed data movement between processors. We describe how typical MapReduce functionality can be implemented in an MPI context, and also in an out-of-core manner for data sets that do not fit within the aggregate memory of a parallel machine. Our motivation for creating this library was to enable graph algorithms to be written as MapReduce operations, allowing processing of terabyte-scale data sets on traditional MPI-based clusters. We outline MapReduce versions of several such algorithms: vertex ranking via PageRank, triangle finding, connected component identification, Luby's algorithm for maximally independent sets, and single-source shortest-path calculation. To test the algorithms on arbitrarily large artificial graphs we generate randomized R-MAT matrices in parallel; a MapReduce version of this operation is also described. Performance and scalability results for the various algorithms are presented for varying size graphs on a distributed-memory cluster. For some cases, we compare the results with non-MapReduce algorithms, different machines, and different MapReduce software, namely Hadoop. Our open-source library is written in C++, is callable from C++, C, Fortran, or scripting languages such as Python, and can run on any parallel platform that supports MPI.

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