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Map Reduce is a key-value based programming model and an associated implementation for processing large data sets. It has been adopted in various scenarios and seems promising. However, when spatial computation is expressed straightforward by this key-value based model, difficulties arise due to unfit features and performance degradation. In this paper, we present methods as follows: 1) a splitting method for balancing workload, 2) pending file structure and redundant data partition dealing with relation between spatial objects, 3) a strip-based two-direction plane sweeping algorithm for computation accelerating. Based on these methods, ANN(All nearest neighbors) query and astronomical cross-certification are developed. Performance evaluation shows that the Map Reduce-based spatial applications outperform the traditional one on DBMS.