A similarity join combines vectors based on a distance condition. Typically, such algorithms apply a filter step (by indexing or sorting) and then refine pairs of candidate vectors. In this paper, we propose to refine the pairs in an order defined by a space-filling curve which dramatically improves data locality. Modern multi-core microprocessors are supported by a deep memory hierarchy including RAM, various levels of cache, and registers. The space-filling curve makes our proposed algorithm cache-oblivious to fully exploit the memory hierarchy and to reach the possible peak performance of a multi-core processor. Our novel space-filling curve called Fast General Form (FGF) Hilbert solves a number of limitations of well-known approaches: it is non-recursive, it is not restricted to traverse squares, and it has a constant time and space complexity. As we demonstrate the easy transformation from conventional into cache-oblivious loops we believe that many algorithms for complex joins and other database operators could be transformed systematically into cache-oblivious SIMD and MIMD parallel algorithms.

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