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Enhancing privacy through uniform grid and caching in location-based services

FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2018年 86卷 881-892页

作者： Zhang, Shaobo Choo, Kim-Kwang Raymond Liu, Qin Wang, Guojun Cent S Univ Sch Informat Sci & Engn Changsha 410083 Peoples R China Univ Texas San Antonio Dept Informat Syst & Cyber Secur San Antonio TX 78249 USA Guangzhou Univ Sch Comp Sci & Educ Software Guangzhou 510006 Guangdong Peoples R China Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Hunan Peoples R China Hunan Univ Sci & Technol Sch Comp Sci & Engn Xiangtan 411201 Peoples R China

With the increasing popularity of location-based services (LBSs), there is a corresponding increase in the potential for location privacy leakage. Existing solutions generally introduce a fully-trusted third party between the users and the location service provider (LSP). However, such an approach offers limited privacy guarantees and incurs high communication overhead. Specifically, once a fully-trusted third party is compromised, user information would likely be exposed. In this paper, we propose a solution designed to enhance location privacy in LBSs. Our scheme is based on the uniform grid, and adopts both order preserving symmetric encryption (OPSE) and k-anonymity technique. Thus, the anonymizer knows nothing about a user's real location, and it can only implement simple matching and comparison operations. In our approach, we also employ an entity (hereafter referred to as the converter) to transform the user defined grid structure into the uniform grid structure. This combined with the caching mechanism, allow us to avoid repeated queries from different users on the same query spatial region and consequently, reduce the overhead of the LBS server. The analysis and simulation results demonstrate that our proposal can effectively preserve a user's location privacy, with reduced overheads at the anonymizer and the LBS server. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Location privacy uniform grid Caching Order-preserving symmetric encryption (OPSE) k-anonymity

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Two algorithms for periodic extension on uniform grids

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NUMERICAL ALGORITHMS 2021年第2期86卷 475-494页

作者： Gruberger, Nira Levin, David Ruppin Acad Ctr Emek Heffer Hod Hasharon Israel Tel Aviv Univ Sch Math Sci Tel Aviv Israel

Given function values on a uniform grid in a domain omega in Double-struck capital Rd, one is often interested in extending the values to a larger grid on a box B containing omega. In particular, we are interested in "periodic extensions." For such extensions the discrete Fourier transform (DFT) of the resulting grid values on B is expected to provide good efficient approximation to the underlying function on omega. This paper presents two different extension algorithms. The first method is a natural approach to this problem, aiming at achieving the fastest decay of the DFT coefficients of the extended *** second is a fast algorithm which is appropriate for the univariate case and for limited cases of multivariate scenarios. It is shown that if a "good" periodic extension exists, the proposed method will find an extension with similar properties.

关键词： Extension Fourier coefficients Periodic uniform grid Decay rate

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Extremal Interpolation in the Mean in the Space L1(R) with Overlapping Averaging Intervals

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MATHEMATICAL NOTES 2024年第1-2期115卷 102-113页

作者： Shevaldin, V. T. Russian Acad Sci Krasovskii Inst Math & Mech Ural Branch Ekaterinburg 620990 Russia

On a uniform grid on the real axisR, we study the Yanenko-Stechkin-Subbotinproblem of extremal function interpolation in the mean in the space L-1(R)of two-way real sequenceswith the least value of the norm of a linear formally s This problem is considered for the class ofsequences for which the generalizedfinite differences of order n corresponding to the operator L-n are bounded in the space l(1). In this paper, the least value of the norm is calculated exactly if the gridstephand the averaging step h(1)of the function to be interpolated in the mean are related by the inequalitiesh

关键词： extremal interpolation in the mean spline uniform grid formally self-adjoint differential operator least norm

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Richardson's Third-Order Difference Scheme for the Cauchy Problem in the Case of Transport Equation

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2024年第10期64卷 2212-2221页

作者： Shishkin, G. I. Shishkina, L. P. Russian Acad Sci Ural Branch Inst Math & Mech Ekaterinburg 620990 Russia

The Cauchy problem for the regular transport equation is considered. Using Richardson's technique, a difference scheme of improved accuracy order on three embedded grids is constructed for this problem. This schem... 详细信息

关键词： transport equation Cauchy problem standard difference scheme uniform grid residual expansion of residual monotonicity of differential and grid problems Richardson's technique difference scheme improved accuracy order convergence in the maximum norm

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Local Extremal Interpolation on the Semiaxis with the Least Value of the Norm for a Linear Differential Operator

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MATHEMATICAL NOTES 2023年第3-4期113卷 446-452页

作者： Shevaldin, V. T. Russian Acad Sci NN Krasovskii Inst Math & Mech Ural Branch Ekaterinburg 620990 Russia

On a uniform grid of nodes on the semiaxis [0;+infinity), a generalization is considered of Yu. N. Subbotin's problem of local extremal functional interpolation of numerical sequences y = {yk}(k=0)(infinity) that have bounded generalized finite differences corresponding to a linear differential operator L-n of order n and whose first terms y(0), y(1),..., y(s-1) are predefined. Here it is required to find an n times differentiable function f such that f(kh) = y(k) (k is an element of Z(+), h > 0) which has the least norm of the operator L-n in the space L-infinity. For linear differential operators with constant coefficients for which all roots of the characteristic polynomial are real and pairwise distinct, it is proved that this least norm is finite only in the case of s >= n.

关键词： local interpolation differential operator generalized finite difference semiaxis uniform grid

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An Improved Difference Scheme for the Cauchy Problem in the Case of a Transport Equation

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2023年第8期63卷 1401-1407页

作者： Shishkin, G. I. Shishkina, L. P. Russian Acad Sci Krasovskii Inst Math & Mech Ural Branch Ekaterinburg 620108 Russia

The Cauchy problem for the regular transport equation is considered. The Richardson technique is used to construct an improved difference scheme that converges in the maximum norm with the second order of convergence.

关键词： transport equation Cauchy problem standard difference scheme uniform grid residual expansion of residual monotonicity of differential and grid problems Richardson technique improved difference scheme convergence in the maximum norm

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Maxima and minima of homogeneous Gaussian random fields over continuous time and uniform grids

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STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES 2020年第2期92卷 165-192页

作者： Lu, Yingyin Peng, Zuoxiang Southwest Univ Sch Math & Stat Chongqing Peoples R China

In this paper, for centred homogeneous Gaussian random fields the joint limiting distributions of normalized maxima and minima over continuous time and uniform grids are investigated. It is shown that maxima and minima are asymptotic dependent for strongly dependent homogeneous Gaussian random field with the choice of sparse grid, Pickands' grid or dense grid, while for the weakly dependent Gaussian random field maxima and minima are asymptotically independent.

关键词： Maximum and minimum joint limit distribution continuous time uniform grid homogeneous Gaussian random field

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Effects of spatial decomposition on the efficiency of kNN search in spatial interpolations

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INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS 2022年第1期37卷 103-121页

作者： Fan Naijie Mei Gang Ding Zengyu Cuomo, Salvatore Xu Nengxiong China Univ Geosci Beijing Sch Engn & Technol Beijing 100083 Peoples R China Univ Naples Federico II Dept Math & Applicat Naples Italy

Spatial interpolations are commonly used in geometric modelling in life science applications such as medical image processing. In large-scale spatial interpolations, it is always needed to find a local set of data points for each interpolated point using the k Nearest Neighbor (kNN) search. To improve the efficiency of kNN, the uniform grid is commonly employed to fastly locate neighbours, and the size of grid cell could strongly affect the efficiency of kNN search. In this paper, we evaluate effects of the size of uniform grid cell on the efficiency of kNN search which is implemented on the CPU and GPU. We employ the Standard Deviation of points' coordinates to measure the spatial distribution of scattered points. For irregularly distributed scattered points, we perform several series of kNN search in two- and three-dimensions. Benchmark results indicate that: for both the sequential version implemented on the CPU and the parallel version implemented on the GPU, with the increase of the Standard Deviation of points' coordinates, the relatively optimal size of the grid cell decreases and eventually converges. Moreover, relationships between the Standard Deviation of scattered points' coordinates and the relatively optimal size of grid cell are fitted. [GRAPHICS] .

关键词： Spatial interpolation k nearest neighbours (kNN) search uniform grid spatial distribution standard deviation

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A Difference Scheme of the Decomposition Method for an Initial Boundary Value Problem for the Singularly Perturbed Transport Equation

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2022年第7期62卷 1193-1201页

作者： Shishkin, G., I Shishkina, L. P. Russian Acad Sci Inst Math & Mech Ural Branch Ekaterinburg 620108 Russia

An initial boundary value problem for the singularly perturbed transport equation is considered. A new approach to constructing the difference scheme based on a special decomposition of solution into the sum of a regular and a singular components is proposed. A difference scheme is constructed based on the solution decomposition method in which the regular and singular components of the solution are considered on uniform grids, and their epsilon-uniform convergence in the maximum norm with the first order of the convergence rate is proved. Given the grid solutions for the components, a continual solution that approximates the solution of the initial boundary value problem for the singularly perturbed transport equation is constructed, and its epsilon-uniform convergence in the maximum norm with the first order of the convergence rate is proved. The proposed approach will make it possible to use the technique of improving the convergence rate of grid solutions on embedded grids for constructing difference schemes that converge epsilon-uniformly with the second-order rate and higher for the initial boundary value problem for the singularly perturbed transport equation.

关键词： transport equation singularly perturbed initial boundary value problem boundary layer standard difference scheme decomposition of solution uniform grid epsilon-uniform convergence maximum norm continual approximation of solution

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Toward Answering Federated Spatial Range Queries Under Local Differential Privacy

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INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2024年第1期2024卷

作者： Feng, Guanghui Wang, Guojun Peng, Tao Guangzhou Univ Sch Comp Sci & Cyber Engn Guangzhou 510006 Peoples R China

Federated analytics (FA) over spatial data with local differential privacy (LDP) has attracted considerable research attention recently. Existing solutions for this problem mostly employ a uniform grid (UG) structure, which recursively decomposes the whole spatial domain into fine-grained regions in the distributed setting. In each round, the sampled clients perturb their locations using a random response mechanism with a fixed probability. This approach, however, cannot encode the client's location effectively and will lead to ill-suited query results. To address the deficiency of existing solutions, we propose LDP-FSRQ, a spatial range query algorithm that relies on a hybrid spatial structure composed of the UG and quad-tree with nonuniform perturbation (NUP) probability to encode and perturb clients' locations. In each iteration of LDP-FSRQ, each client adopts the quad-tree to encode his/her location into a binary string and uses four local perturbation mechanisms to protect the encoded string. Then, the collector prunes the quad-tree of the current round according to the clients' reports and shares the pruned tree with the clients of the next round. We demonstrate the application of LDP-FSRQ on Beijing, Landmark, Check-in, and NYC datasets, and the experimental results show that our approach outperforms its competitors in terms of queries' utility.

关键词： federated analytics local differential privacy quad-tree spatial data release spatial range queries uniform grid

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