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Abstract
We consider a new construction of localitysensitive hash functions for Hamming space that is covering in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius r. The construction is efficient in the sense that the expected number of hash collisions between vectors at distance cr, for a given c>1, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (STOC’98). The efficiency of the new construction essentially matches their bound when the search radius is not too large—e.g., when cr = o(log (n)/ log log n), where n is the number of points in the dataset, and when cr = log (n)/k, where k is an integer constant. In general, it differs by at most a factor ln (4) in the exponent of the time bounds. As a consequence, LSHbased similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency.
Original language  English 

Article number  29 
Journal  A C M Transactions on Algorithms 
Volume  14 
Issue number  3 
ISSN  15496325 
DOIs  
Publication status  Published  2018 
Keywords
 recall
 localitysensitive hashing
 highdimensional
 Similarity search
 Theory of computation
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Dive into the research topics of 'CoveringLSH: Localitysensitive Hashing without False Negatives'. Together they form a unique fingerprint.Projects
 1 Finished

SSS: Scalable Similarity Search
Pagh, R. (PI), Christiani, T. L. (CoI), Pham, N. D. (CoI), Faithfull, A. (CoI), Silvestri, F. (CoI), Mikkelsen, J. W. (CoI), Sivertsen, J. V. T. (CoI), Aumüller, M. (CoI), Skala, M. (CoI), Ceccarello, M. (CoI), Themsen, R. (CoI), Jacob, R. (CoI), McCauley, S. (CoI) & Ahle, T. D. (CoI)
01/05/2014 → 30/04/2019
Project: Research