Locality-sensitive Hashing Without False Negatives For L_p
Pacuk Andrzej, Sankowski Piotr, Wegrzycki Karol, Wygocki Piotr. Computing and Combinatorics - 2016
[Paper]
Independent
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 in dimensional space equipped with norm
when . Furthermore, we show how to use these hash functions
to solve the -approximate nearest neighbor search problem without false
negatives. Namely, if there is a point at distance , we will certainly
report it and points at distance greater than will not be reported for
. The constructed algorithms work: - with
preprocessing time and sublinear expected query time,
- with preprocessing time and expected query
time . Our paper reports progress on answering the open
problem presented by Pagh [8] who considered the nearest neighbor search
without false negatives for the Hamming distance.
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