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Locality-sensitive Hashing Without False Negatives For L_p

Pacuk Andrzej, Sankowski Piotr, Wegrzycki Karol, Wygocki Piotr. Computing and Combinatorics - 2016

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In this paper, we show a construction of locality-sensitive hash functions without false negatives, i.e., which ensure collision for every pair of points within a given radius R in d dimensional space equipped with lp norm when p[1,]. Furthermore, we show how to use these hash functions to solve the c-approximate nearest neighbor search problem without false negatives. Namely, if there is a point at distance R, we will certainly report it and points at distance greater than cR will not be reported for c=Ω(d,d11p). The constructed algorithms work: - with preprocessing time O(nlog(n)) and sublinear expected query time,

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