I/o-efficient Similarity Join

Pagh Rasmus, Pham Ninh, Silvestri Francesco, Stöckel Morten. Arxiv 2015

[Paper]    
ARXIV Independent LSH

We present an I/O-efficient algorithm for computing similarity joins based on locality-sensitive hashing (LSH). In contrast to the filtering methods commonly suggested our method has provable sub-quadratic dependency on the data size. Further, in contrast to straightforward implementations of known LSH-based algorithms on external memory, our approach is able to take significant advantage of the available internal memory: Whereas the time complexity of classical algorithms includes a factor of $N^{\rho }$, where $\rho$ is a parameter of the LSH used, the I/O complexity of our algorithm merely includes a factor $(N/M{)}^{\rho }$, where $N$ is the data size and $M$ is the size of internal memory. Our algorithm is randomized and outputs the correct result with high probability. It is a simple, recursive, cache-oblivious procedure, and we believe that it will be useful also in other computational settings such as parallel computation.

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