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This paper presents a grid-enabled MapReduce framework called ''Ussop''. Ussop provides its users with a set of C-language based MapReduce APIs and an efficient runtime system for exploiting the computing resources available on public-resource grids. Considering the volatility nature of the grid environment, Ussop introduces two novel task scheduling algorithms, namely, Variable-Sized Map Scheduling (VSMS) and Locality-Aware Reduce Scheduling (LARS). VSMS dynamically adjusts the size of map tasks according to the computing power of grid nodes. Moreover, LARS minimizes the data transfer cost of exchanging the intermediate data over a wide-area network. The experimental results indicate that both VSMS and LARS achieved superior performance than the conventional scheduling algorithms.