The Algebraic Path Problem on the Cell/B.E. Processor

Report Date: Written Language: Any Other Identifying Information of this Report: Distribution Statement: Supplementary Notes: The University of Aizu Aizu-Wakamatsu Fukushima 965-8580 Japan 11/30/2010 English First Issue: 10 copies Kazuya Matsumoto, Stanislav G. Sedukhin The Algebraic Path Problem on the Cell/B.E. Processor algebraic path problem, all-pairs shortest paths problem, Cell Broadband Engine, performance evaluation, parallel computing The Algebraic Path Problem (APP) unifies well-known matrix, graph, and language problems, such as matrix inversion, all-pairs shortest paths (APSP), maximum capacity paths (MCP), minimum spanning tree, generation of regular languages, etc., into a single algorithmic scheme. The difference between APP instances is in the underlying algebraic structure. This paper explores the APP and presents an implementation of a block algorithm for solving the APP on the Cell Broadband Engine (Cell/B.E.) heterogeneous multicore processor. The block APP algorithm spends the most computing time in a block matrix-matrix multiply-add (MMA) operation in different algebras. In our APP algorithm, a fast dense MMA operation in linear (+,×)-algebra is utilized. The MMA implementation on the Cell/B.E. needs only a single fused multiply-add (FMA) instruction to obtain a single short-vector (+,×)-result in one cycle. APP instances such as APSP and MCP problems are based on (min, +)and (max, min)-algebras, respectively, which are different from the linear (+,×)-algebra, and require three and four instructions to obtain a single short-vector result in three and four cycles. Because of that, the maximum sustained performance for MMA operation on Cell/B.E. is 152 Gflop/s whereas for APSP and MCP are 50.7 Gflop/s and 38.1 Gflop/s, respectively. Manuscript submitted to Journal of Information Processing (IPSJJIP) Distributed Parallel Processing Laboratory The Algebraic Path Problem on the Cell/B.E. Processor Kazuya Matsumoto Stanislav G. Sedukhin

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