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To achieve cost-savings, data owners outsource their spatio-textual query services to public cloud, which, however, may bring serious privacy issues. In this paper, we define and study the problem of privacy-preserving spatio-textual skylines in cloud environments. To address the problem, we first transform the locations and texts of each data object and query request into vectors and encrypt the vectors based on an vector-based encryption method to protect the data privacy. Exploiting the group of query locations to accelerate the query processing, we further present a location-aggregation-based query request generation method. Based on encrypted aggregated query requests, we present a corresponding query processing algorithm for privacy-preserving spatio-textual skylines. Finally, we present analysis to show the security guarantee of the proposed methods, and conduct thorough experiments on real datasets to show the performance of our algorithms.

With massive real-world networks added with spatial attributes, query processing in spatial networks has been widely used in real-life applications. Considering the high costs of spatial network queries, outsourcing querying services to cloud provides a cost-effective way for data owners. However, directly outsourcing such services may cause serious privacy concerns. To address this privacy problem, existing studies apply anonymous or differential privacy techniques on spatial network queries, which are not under the semi-trusted secure model. Other existing works primarily focus on query processing over either encrypted spatial or network data, which cannot directly be applied to work out the secure spatial network query problem. To this end, we define and study Secure Spatial Network kNN Query (SSNQ) problem on cloud platform. We first present Basic Secure Spatial Network kNN Query (BSSNQ) method, in which we compute secure kNN for the query node to construct candidate sequences using secure subprotocols. With pre-encrypted network distances, we then compute shortest paths between the query node and each candidate, and securely update the candidate sequences according to Euclidean restriction to derive final query results. To improve the efficiency of BSSNQ, we further propose Heuristic Secure Spatial Network kNN Query (HSSNQ) method, which securely calculates shortest paths from the query node to the visiting nodes iteratively, and use optimistic estimate distances as the key to lead the heuristic search within a priority queue. Thorough analysis shows the security and complexity of the proposed methods, and extensive experimental results on real datasets demonstrate the efficiency of the query performance.

Circle curve fitting is always the important issue of the engineering technology. The effect of circle curve fitting is influenced by both the data quality and fitting method. In this paper, using the special properties of circle, that's the error value of any two radius is zero. Then the method of circle curve fitting was proposed, by finding the minimum error distance between any two fitting points and the fitted center points. Under various test data points, both our algorithm and other classical algorithms can get accurate circle fitting. Especially, the method of this paper can get more accurate results, under the situation that the degree of dispersion of the fitting points is bigger and the radian of the fitting points is smaller.