Queries on spatial data commonly concern a certain range or area, for example, queries related to intersections, containment and nearest neighbors. The Continuous Nearest Neighbor (CNN) query is one kind of the nearest neighbor queries. For example, people may want to know where those gas stations are along the super highway from the starting position to the ending position. Due to that there is no total ordering of spatial proximity among spatial objects, the space filling curve (SFC) approach has proposed to preserve the spatial locality. Chen and Chang have proposed efficient algorithms based on SFC to answer nearest neighbor queries, so we may perform a sequence of individually nearest neighbor queries to answer such a CNN query in the centralized system by one of Chen and Chang's algorithms. However, each searched range of these nearest neighbor queries could be overlapped, and these queries may access several same pages on the disk, resulting in many redundant disk accesses. On the other hand, Zheng et al. have proposed an algorithm based on the Hilbert curve for the CNN query for the wireless broadcast environment, and it contains two phases. In the first phase, Zheng et al.'s algorithm designs a searched range to find candidate objects. In the second phase, it uses some heuristics to filter the candidate objects for the final answer. However, Zheng et al.'s algorithm may check some data blocks twice or some useless data blocks, resulting in some redundant disk accesses. Therefore, in this thesis, to avoid these disadvantages in the first phase of Zheng et al.'s algorithm, we propose a local expansion approach based on the Peano curve for the CNN query in the centralized system. In the first phase, we determine the searched range to obtain all candidate objects. Basically, we first calculate the route between the starting point and the ending point. Then, we move forward one block from the starting point to the ending point, and locally spread the searched range to find the candidate objects. In the second phase, we use heuristics mentioned in Zheng et al.'s algorithm to filter the candidate objects for the final answer. Based on such an approach, we proposed two algorithms: the forward moving (FM) algorithm and the forward moving* (FM*) algorithm. The FM algorithm assumes that each object is in the center of a block, and the FM* algorithm assumes that each object could be in any place of a block. Our local expansion approach can avoid the duplicated check in Zheng et al.'s algorithm, and determine a searched range with higher accuracy than that of Zhenget al.'s algorithm. From our simulation results, we show that the performance of the FM or FM* algorithm is better than that of Zheng et al.'s algorithm, in terms of the accuracy and the processing time.

Increasing numbers of people are subscribing to location-based services, but as the popularity grows so are the privacy concerns. Varieties of research exist to address these privacy concerns. Each technique tries to address different models with which location-based services respond to subscribers. In this work, we present ideas to address privacy concerns for the two main models namely: the snapshot nearest neighbor query model and the continuous nearest neighbor query model. First, we address snapshot nearest neighbor query model where location-based services response represents a snapshot of point in time. In this model, we introduce a novel idea based on the concept of an open set in a topological space where points belongs to a subset called neighborhood of a point. We extend this concept to provide anonymity to real objects where each object belongs to a disjointed neighborhood such that each neighborhood contains a single object. To help identify the objects, we implement a database which dynamically scales in direct proportion with the size of the neighborhood. To retrieve information secretly and allow the database to expose only requested information, private information retrieval protocols are executed twice on the data. Our study of the implementation shows that the concept of a single object neighborhood is able to efficiently scale the database with the objects in the area. The size of the database grows with the size of the grid and the objects covered by the location-based services. Typically, creating neighborhoods, computing distances between objects in the area, and running private information retrieval protocols causes the CPU to respond slowly with this increase in database size. In order to handle a large number of objects, we explore the concept of kernel and parallel computing in GPU. We develop GPU parallel implementation of the snapshot query to handle large number of objects. In our experiment, we exploit parameter tuning. The results show that with parameter tuning and parallel computing power of GPU we are able to significantly reduce the response time as the number of objects increases. To determine response time of an application without knowledge of the intricacies of GPU architecture, we extend our analysis to predict GPU execution time. We develop the run time equation for an operation and extrapolate the run time for a problem set based on the equation, and then we provide a model to predict GPU response time. As an alternative, the snapshot nearest neighbor query privacy problem can be addressed using secure hardware computing which can eliminate the need for protecting the rest of the sub-system, minimize resource usage and network transmission time. In this approach, a secure coprocessor is used to provide privacy. We process all information inside the coprocessor to deny adversaries access to any private information. To obfuscate access pattern to external memory location, we use oblivious random access memory methodology to access the server. Experimental evaluation shows that using a secure coprocessor reduces resource usage and query response time as the size of the coverage area and objects increases. Second, we address privacy concerns in the continuous nearest neighbor query model where location-based services automatically respond to a change in object*s location. In this model, we present solutions for two different types known as moving query static object and moving query moving object. For the solutions, we propose plane partition using a Voronoi diagram, and a continuous fractal space filling curve using a Hilbert curve order to create a continuous nearest neighbor relationship between the points of interest in a path. Specifically, space filling curve results in multi-dimensional to 1-dimensional object mapping where values are assigned to the objects based on proximity. To prevent subscribers from issuing a query each time there is a change in location and to reduce the response time, we introduce the concept of transition and update time to indicate where and when the nearest neighbor changes. We also introduce a database that dynamically scales with the size of the objects in a path to help obscure and relate objects. By executing the private information retrieval protocol twice on the data, the user secretly retrieves requested information from the database. The results of our experiment show that using plane partitioning and a fractal space filling curve to create nearest neighbor relationships with transition time between objects reduces the total response time.