2,834 research outputs found

    Tradeoffs for nearest neighbors on the sphere

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    We consider tradeoffs between the query and update complexities for the (approximate) nearest neighbor problem on the sphere, extending the recent spherical filters to sparse regimes and generalizing the scheme and analysis to account for different tradeoffs. In a nutshell, for the sparse regime the tradeoff between the query complexity nρqn^{\rho_q} and update complexity nρun^{\rho_u} for data sets of size nn is given by the following equation in terms of the approximation factor cc and the exponents ρq\rho_q and ρu\rho_u: c2ρq+(c2βˆ’1)ρu=2c2βˆ’1.c^2\sqrt{\rho_q}+(c^2-1)\sqrt{\rho_u}=\sqrt{2c^2-1}. For small c=1+Ο΅c=1+\epsilon, minimizing the time for updates leads to a linear space complexity at the cost of a query time complexity n1βˆ’4Ο΅2n^{1-4\epsilon^2}. Balancing the query and update costs leads to optimal complexities n1/(2c2βˆ’1)n^{1/(2c^2-1)}, matching bounds from [Andoni-Razenshteyn, 2015] and [Dubiner, IEEE-TIT'10] and matching the asymptotic complexities of [Andoni-Razenshteyn, STOC'15] and [Andoni-Indyk-Laarhoven-Razenshteyn-Schmidt, NIPS'15]. A subpolynomial query time complexity no(1)n^{o(1)} can be achieved at the cost of a space complexity of the order n1/(4Ο΅2)n^{1/(4\epsilon^2)}, matching the bound nΞ©(1/Ο΅2)n^{\Omega(1/\epsilon^2)} of [Andoni-Indyk-Patrascu, FOCS'06] and [Panigrahy-Talwar-Wieder, FOCS'10] and improving upon results of [Indyk-Motwani, STOC'98] and [Kushilevitz-Ostrovsky-Rabani, STOC'98]. For large cc, minimizing the update complexity results in a query complexity of n2/c2+O(1/c4)n^{2/c^2+O(1/c^4)}, improving upon the related exponent for large cc of [Kapralov, PODS'15] by a factor 22, and matching the bound nΞ©(1/c2)n^{\Omega(1/c^2)} of [Panigrahy-Talwar-Wieder, FOCS'08]. Balancing the costs leads to optimal complexities n1/(2c2βˆ’1)n^{1/(2c^2-1)}, while a minimum query time complexity can be achieved with update complexity n2/c2+O(1/c4)n^{2/c^2+O(1/c^4)}, improving upon the previous best exponents of Kapralov by a factor 22.Comment: 16 pages, 1 table, 2 figures. Mostly subsumed by arXiv:1608.03580 [cs.DS] (along with arXiv:1605.02701 [cs.DS]

    Worst case QC-MDPC decoder for McEliece cryptosystem

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    McEliece encryption scheme which enjoys relatively small key sizes as well as a security reduction to hard problems of coding theory. Furthermore, it remains secure against a quantum adversary and is very well suited to low cost implementations on embedded devices. Decoding MDPC codes is achieved with the (iterative) bit flipping algorithm, as for LDPC codes. Variable time decoders might leak some information on the code structure (that is on the sparse parity check equations) and must be avoided. A constant time decoder is easy to emulate, but its running time depends on the worst case rather than on the average case. So far implementations were focused on minimizing the average cost. We show that the tuning of the algorithm is not the same to reduce the maximal number of iterations as for reducing the average cost. This provides some indications on how to engineer the QC-MDPC-McEliece scheme to resist a timing side-channel attack.Comment: 5 pages, conference ISIT 201

    Efficient storage and decoding of SURF feature points

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    Practical use of SURF feature points in large-scale indexing and retrieval engines requires an efficient means for storing and decoding these features. This paper investigates several methods for compression and storage of SURF feature points, considering both storage consumption and disk-read efficiency. We compare each scheme with a baseline plain-text encoding scheme as used by many existing SURF implementations. Our final proposed scheme significantly reduces both the time required to load and decode feature points, and the space required to store them on disk
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