Quadtree Index Research Articles

Efficient and Privacy-Preserving Arbitrary Polygon Range Query Scheme Over Dynamic and Time-Series Location Data

Location-based services (LBSs) provide enhanced functionality of mobile applications and convenience for mobile users, which plays a more and more remarkable role in people’s daily life. In LBSs, spatial range query is an essential tool for users to find interesting points in a specific region. However, during spatial range query, it is necessary for data owners and query users to exchange their location data, and the leakage of private location information has drawn significant attention in both governmental and social aspects. Meanwhile, most existing location privacy protection schemes only focus on achieving regular geometry range query over static location datasets. In this paper, we present an efficient and privacy-preserving arbitrary polygon range query scheme, named EPAPRQ. With EPAPRQ, the arbitrary and fine-grained polygon range query can be executed over a dynamic and time-series location dataset with privacy protection. Specifically, in EPAPRQ, an arbitrary polygon range query algorithm is first introduced with sub-range query technique. Then, to protect the private location information of the data owner and query users, a series privacy-preserving data computation protocols are constructed with a symmetric homomorphic encryption algorithm, and a ciphertext-based location dataset updating strategy is also designed. Finally, we propose a double filtration method through combining the quadtree index structure and minimum bounded rectangle, which is able to greatly improve the query efficiency over ciphertexts. Detailed security analysis shows that the sensitive location information in EPAPRQ can be well protected. Furthermore, we evaluate the performance of EPAPRQ in the real map, and the results demonstrate that EPAPRQ is indeed efficient.

Interactive Visualization of Geographic Vector Big Data Based on Viewport Generalization Model

The visualization of geographic vector data is an important premise for spatial analysis and spatial cognition. Traditional geographic vector data visualization methods are data-driven, and their computational costs have increased rapidly with the growth of the scale of data used. Even if the distributed parallel strategy is used, it is still difficult to achieve a real-time response when dealing with big geographic vector data (BGVD). To solve this problem, this paper proposes a viewport generalization model and a visualization method for the online interactive visualization of BGVD. The method takes the viewport display pixel as the analysis unit and synthesizes the existence or quantity results of geographic vector data in the corresponding spatial range of each viewport display pixel into the display value of this display pixel; thus, it converts traditional computational complexity, dependent on the data scale, into computational complexity dependent on the number of pixels in the viewport. When the number of pixels in the viewport is much smaller than that of the geographic vector data, the visualization efficiency is greatly improved. In order to realize the above conversion, the pixel quadtree index (VPQ) structure and the real-time visualization algorithm of geographic vector data based on VPQ are proposed. Experiments show that the proposed method can achieve the near-real-time interactive visualization of BGVD, and provides more than a tenfold performance improvement over the best existing methods.

A Visualization and Analysis Method by Multi-Dimensional Crossplots from Multi-Well Heterogeneous Data

Crossplot is an important tool for data visualization analysis in well logging processing and interpretation. Generally, the color of the points in the crossplot is calibrated by the data to improve the plane crossplot from two dimensions (2D) to three dimensions (3D). However, this method is limited to the logging data. In many cases, it is necessary to use crossplots for comprehensive evaluation with the well logging, geology, mud logging, and oil testing data, or to deeply analyze the data from multiple wells and multiple layers. The traditional crossplots cannot meet the demands. To expand the traditional crossplot to multiple dimensions, we proposed an augmented-dimensional visualization and analysis method by the crossplot with multi-well and multi-dimensional heterogeneous data, which is developed based on the traditional crossplots. Firstly, we built the match matrix of the augmented-dimensional heterogeneous data from different depths and set up the crossplots of the heterogeneous data after depth normalization. In this way, the attribute calibrations of the points in the crossplots by logging data were realized, and the auxiliary figures of the augmented-dimensional crossplots were established. In addition, the crossplots were expanded to more dimensions by collaborative analysis of the multiple crossplots and synchronous display in different single-well and multi-well modules with the feature points projection. Secondly, we established the display method of the crossplots from multi-well data by quadtree index. The display and interaction performance of the augmented-dimensional crossplots under the conditions of large amount of data from multiple wells were greatly improved by optimizing the overlapped and covered points in the crossplots. This method can provide more information about the reservoirs and realize the comprehensive well logging comparison, analysis, and visualization from different views. It has been developed and integrated into a CIFLog software platform and has been widely used in many domestic oilfields.

Construction of integration model for regional sub-metre high-resolution remote sensing geographic information

In order to overcome the problem of poor data coordination existing in the existing geographic information integration model, a new regional sub-metre high score remote sensing geographic information integration model construction method is proposed. The application of distributed integration technology to build a regional sub-metre level high score remote sensing geographic information integration model. Joint processing of images, in the integrated environment of GIS and RS, transform the independent variables in the data into a vector grid integrated structure, establish a joint index format based on B+ tree index and quadtree index, complete the RS and GIS model build. Experimental results show that the model can apply street, city name, and place type keywords, with better integrated indexing effect and higher data coordination.

Privacy-Preserving Boolean Range Query with Temporal Access Control in Mobile Computing

With increasingly popular GPS-equipped mobile devices (e.g., smartphones, tablets, laptops), massive spatio-textual data has been outsourced to cloud servers for storage and analysis such as spatial keyword search. However, existing privacy-preserving spatial keyword query schemes only support coarse-grained non-temporal access control in single-user sharing scenarios, which does not scale well in time-related scenes such as message valid period. To solve the above issues, we propose Privacy-preserving Boolean Range Query with Temporal access control in mobile computing (PBRQ-T). Specifically, we first achieve PBRQ with linear search complexity using the adapted Gray code, Bloom filter, and Katz-Sahai-Waters encryption. Then, we provide fine-grained and temporal access control in PBRQ based on the forward/backward derivation function and attribute-based encryption, where PBRQ is executed only when the spatio-textual data is accessible. Finally, an enhanced PBRQ-T (i.e., PBRQ-T+) with faster-than-linear search complexity is proposed by constructing a Quadtree index structure. Our formal security analysis shows that data privacy and index privacy can be guaranteed during the query process. Our extensive experiments using a real-world dataset demonstrate the efficiency and feasibility of our schemes.

Place Retrieval in Knowledge Graph

With the rapid development of Internet and big data, place retrieval has become an indispensable part of daily life. However, traditional retrieval technology cannot meet the semantic needs of users. Knowledge graph has been introduced into the new-generation retrieval systems to improve retrieval performance. Knowledge graph abstracts things into entities and establishes relationships among entities, which are expressed in the form of triples. However, with the expansion of knowledge graph and the rapid increase of data volume, traditional place retrieval methods on knowledge graph have low performance. This paper designs a place retrieval method in order to improve the efficiency of place retrieval. Firstly, perform data preprocessing and problem model building in the offline stage. Meanwhile, build semantic distance index, spatial quadtree index, and spatial semantic hybrid index according to semantic and spatial information. At the same time, in the online retrieval stage, this paper designs an efficient query algorithm and ranking model based on the index information constructed in the offline stage, aiming at improving the overall performance of the retrieval system. Finally, we use experiment to verify the effectiveness and feasibility of the place retrieval method based on knowledge graph in terms of retrieval accuracy and retrieval efficiency under the real data.

Index-Based Solutions for Efficient Density Peak Clustering

Density Peak Clustering (DPC), a popular density-based clustering approach, has received considerable attention from the research community primarily due to its simplicity and fewer-parameter requirement. However, the resultant clusters obtained using DPC are influenced by the sensitive parameter <inline-formula><tex-math notation="LaTeX">$d_c$</tex-math></inline-formula> , which depends on data distribution and requirements of different users. Besides, the original DPC algorithm requires visiting a large number of objects, making it slow. To this end, this paper investigates index-based solutions for DPC. Specifically, we propose two list-based index methods viz. (i) a simple List Index, and (ii) an advanced Cumulative Histogram Index. Efficient query algorithms are proposed for these indices which significantly avoids irrelevant comparisons at the cost of space. For memory-constrained systems, we further introduce an approximate solution to the above indices which allows substantial reduction in the space cost, provided that slight inaccuracies are admissible. Furthermore, owing to considerably lower memory requirements of existing tree-based index structures, we also present effective pruning techniques and efficient query algorithms to support DPC using the popular Quadtree Index and R-tree Index. Finally, we practically evaluate all the above indices and present the findings and results, obtained from a set of extensive experiments on six synthetic and real datasets. The experimental insights obtained can help to guide in selecting a befitting index.

ESPM: Efficient Spatial Pattern Matching

With recent advances in information technologies such as global position system and mobile internet, a huge volume of spatio-textual objects have been generated from location-based services, which enable a wide range of spatial keyword queries. Recently, researchers have proposed a novel query, called Spatial Pattern Matching (SPM), which uses a pattern to capture the user's intention. It has been demonstrated to be fundamental and useful for many real applications. Despite its usefulness, the SPM problem is computationally intractable. Existing algorithms suffer from the low efficiency issue, especially on large scale datasets. To enhance the performance of SPM, in this paper we propose a novel Efficient Spatial Pattern Matching (ESPM) algorithm, which exploits the inverted linear quadtree index and computes matched node pairs and object pairs level by level in a top-down manner. In particular, it focuses on pruning unpromising nodes and node pairs at the high levels, resulting in a large number of unpromising objects and object pairs to be pruned before accessing them from disk. We experimentally evaluate the performance of ESPM on real large datasets. Our results show that ESPM is over one order of magnitude faster than the state-of-the-art algorithm, and also uses much less I/O cost.

Real-Time Displacement of Point Symbols Based on Spatial Distribution Characteristics

Maps at different scales have different emphases on the information representation of point data. With a focus on large scales, this paper proposes an improved sequential displacement method. While existing approaches mostly use a fixed order to place points during displacement, the proposed method takes into consideration the spatial distribution characteristics, including the spatial structure and the holistic distance relations of a point group. This method first rapidly extracts feature points through a quadtree index to capture the spatial structure of a point group. Then, it uses map information content to determine the points to be processed. Finally, a global distance matrix for the above two sets of points is established. Overlapping of symbols is resolved by processing the global distance matrix. The algorithm is estimated by comparing with the latest strategy, which has overcome the position drift drawback of traditional sequential displacement methods and the results show that the proposed method can improve the effects of map expression and meet the requirements of real-time processing.

Location-Based Seeds Selection for Influence Blocking Maximization in Social Networks

Influence blocking maximization (IBM) is a key problem for viral marketing in competitive social networks. Although the IBM problem has been extensively studied, existing works neglect the fact that the location information can play an important role in influence propagation. In this paper, we study the location-based seeds selection for IBM problem, which aims to find a positive seed set in a given query region to block the negative influence propagation in a given block region as much as possible. In order to overcome the low efficiency of the simulation-based greedy algorithm, we propose a heuristic algorithm IS-LSS and its improved version IS-LSS+, both of which are based on the maximum influence arborescence structure and Quadtree index, while IS-LSS+ further improves the efficiency of IS-LSS by using an upper bound method and Quadtree cell lists. The experimental results on real-world datasets demonstrate that our proposed algorithms are able to achieve matching blocking effect to the greedy algorithm as the increase in the number of positive seeds and often better than other heuristic algorithms, whereas they are four orders of magnitude faster than the greedy algorithm.

Distributed continuous KNN query over moving objects

The Continuous K-Nearest Neighbour (CKNN) queries over moving objects have been widely researched in many fields. However, existing centralised works cannot work anymore and distributed solutions suffer the problem of index maintaining, high communication cost and query latency. In this paper, we firstly propose a distributed hybrid indexing strategy which combines the Spatial-temporal Sensitive Grid Index (SSGI) and the dynamic quad-tree index (DQI). The SSGI is proposed to locate the spatial range that contains the final results, and the DQI is used for data partitioning. Then, we introduce an algorithm named HDCKNN to implement the CKNN queries. In comparison of existing work, HDCKNN can achieve the final result in one round iteration, while existing methods require at least two rounds of iteration. Extensive experiments show that the performance of the proposed method is more efficient than state-of-the-art algorithms.

A QUADTREE SPATIAL INDEX METHOD WITH INCLUSION RELATIONS FOR THE INCREMENTAL UPDATING OF VECTOR LANDCOVER DATABASE

Abstract. In vector landcover database, there are a lot of complex polygons with many holes, even nesting holes. In the incremental updating (i.e., using the change-only information to update the land cover database), a new changed parcel usually has 2-dimensional intersections (e.g., overlap, cover, equal and inside, etc.) with several existing regions, automatic updating operations need to identify the affected objects for the new changes at first. If the existing parcels include complex polygons (i.e., the polygon with holes), it is still needed to determine if there are 2-dimensional intersections between the new changed polygon and each holes of the involved complex polygons. The relation between the complex polygon and its holes has not been presented in the current spatial data indexing methods, only the MBB (Minimum Bounding Box) of the exterior ring of the complex polygon has been stored, the non-involved holes can not be filtered at the first step of spatial access methods. As the refinement geometric operation is costly, therefore the updating process for the complex polygons is very complicated and low efficient using the current spatial data indexing methods. In order to solve this problem, an improved quadtree spatial index method is presented in this paper. In this method, the polygons is divided to two categories according to the relations with the quadrant axes, i.e., disjoint to the axes and intersect with the axes. The intersect polygons are still divided to 5 cases according to the intersection position among the polygons and the different level quadrant axes. The intersection polygons are stored in the different level root nodes in our index tree, and five buckets denoted as XpB, XnB, YpB, YnB, XYB are used to store the polygons intersecting the different level quadrant axes respectively. The polygons disjoint to all quadrant axes are stored in the leaf nodes in this method. The authors developed the spatial index structure with inclusion relations and the algorithms of the corresponding index operations (e.g., insert, delete and query) for the complex polygons. The effectiveness of the improved index is verified by an experiment of land cover data incremental updating. Experimental results show that the proposed index method is significantly more efficient than the traditional quadtree index in terms of spatial query efficiency, and the time efficiency of the incremental updating is increased about 3 times using the proposed index method than that using the traditional quadtree index.

Location-Aware Influence Blocking Maximization in Social Networks

In real social networks, it is often the case that opposite opinions, ideas, products, or innovations are propagating simultaneously. Although the competitive influence problem has been extensively studied, existing works neglect the fact that the location information can play an important role in influence propagation. In this paper, we study the location-aware influence blocking maximization (LIBM) problem, which aims to find a positive seed set to maximize the blocked negative influence for a given query region. In order to overcome low efficiency of the greedy algorithm, we propose two heuristic algorithms LIBM-H and LIBM-C based on the quadtree index and the maximum influence arborescence structure. Experimental results on real-world datasets show that both LIBM-H and LIBM-C are able to achieve a matching blocking effect to the greedy algorithm and often better than other heuristic algorithms, whereas they are several orders of magnitude faster than the greedy algorithm.

Location-Based Distance Measures for Geosocial Similarity

This article investigates the problem of geosocial similarity among users of online social networks, based on the locations of their activities (e.g., posting messages or photographs). Finding pairs of geosocially similar users or detecting that two sets of locations (of activities) belong to the same user has important applications in privacy protection, recommendation systems, urban planning, and public health, among others. It is explained and shown empirically that common distance measures between sets of locations are inadequate for determining geosocial similarity. Two novel distance measures between sets of locations are introduced. One is the mutually nearest distance that is based on computing a matching between two sets. The second measure uses a quad-tree index. It is highly scalable but incurs the overhead of creating and maintaining the index. Algorithms with optimization techniques are developed for computing the two distance measures and also for finding the k -most-similar users of a given one. Extensive experiments, using geotagged messages from Twitter, show that the new distance measures are both more accurate and more efficient than existing ones.

Query authentications based on a fixed grid partitioning quad-tree index in LBS big data

Query authentications based on a fixed grid partitioning quad-tree index in LBS big data

A VIRTUAL GLOBE-BASED MULTI-RESOLUTION TIN SURFACE MODELING AND VISUALIZETION METHOD

Abstract. The integration and visualization of geospatial data on a virtual globe play an significant role in understanding and analysis of the Earth surface processes. However, the current virtual globes always sacrifice the accuracy to ensure the efficiency for global data processing and visualization, which devalue their functionality for scientific applications. In this article, we propose a high-accuracy multi-resolution TIN pyramid construction and visualization method for virtual globe. Firstly, we introduce the cartographic principles to formulize the level of detail (LOD) generation so that the TIN model in each layer is controlled with a data quality standard. A maximum z-tolerance algorithm is then used to iteratively construct the multi-resolution TIN pyramid. Moreover, the extracted landscape features are incorporated into each-layer TIN, thus preserving the topological structure of terrain surface at different levels. In the proposed framework, a virtual node (VN)-based approach is developed to seamlessly partition and discretize each triangulation layer into tiles, which can be organized and stored with a global quad-tree index. Finally, the real time out-of-core spherical terrain rendering is realized on a virtual globe system VirtualWorld1.0. The experimental results showed that the proposed method can achieve an high-fidelity terrain representation, while produce a high quality underlying data that satisfies the demand for scientific analysis.

A VIRTUAL GLOBE-BASED MULTI-RESOLUTION TIN SURFACE MODELING AND VISUALIZETION METHOD

The integration and visualization of geospatial data on a virtual globe play an significant role in understanding and analysis of the Earth surface processes. However, the current virtual globes always sacrifice the accuracy to ensure the efficiency for global data processing and visualization, which devalue their functionality for scientific applications. In this article, we propose a high-accuracy multi-resolution TIN pyramid construction and visualization method for virtual globe. Firstly, we introduce the cartographic principles to formulize the level of detail (LOD) generation so that the TIN model in each layer is controlled with a data quality standard. A maximum z-tolerance algorithm is then used to iteratively construct the multi-resolution TIN pyramid. Moreover, the extracted landscape features are incorporated into each-layer TIN, thus preserving the topological structure of terrain surface at different levels. In the proposed framework, a virtual node (VN)-based approach is developed to seamlessly partition and discretize each triangulation layer into tiles, which can be organized and stored with a global quad-tree index. Finally, the real time out-of-core spherical terrain rendering is realized on a virtual globe system VirtualWorld1.0. The experimental results showed that the proposed method can achieve an high-fidelity terrain representation, while produce a high quality underlying data that satisfies the demand for scientific analysis.

Research of Embedded GIS Data Management Strategies for Large Capacity

With the use of data for embedded GIS system continues to increase and the requirement of application for embedded GIS system continues to improve, the quad-tree index algorithms and block classification data organization mode that are currently used to handle large amounts of data reflects a certain limitation. combining the characteristics of embedded GIS data, the author put forward the multi-level data indexing and dynamic data loading ,and realize the data loading when required, and enhance the real-time response speed, solves the limitation on large volume data. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3967

A New Organization and Indexing Method of Multibeam Point Cloud Data in 3D Marine GIS

Multibeam sounding system can be used for the acquisition of high-precision digital seabed terrain model, it brings new opportunities for the development of 3D marine GIS (Geographic Information System). But its massive point cloud data poses great challenge for its storage and visualization. This paper proposes a new storage strategy and gives an optimized visualization method specifically for the storage strategy. First, we take advantage of the point cloud coordinates regularity to sort these points according to certain rules and efficiently organize it through multiple spatial index. Vertically, a multi-level pyramid index is established. We generate a number of levels data with different level of detail and different scale, namely the static level of detail (LOD) model, in this way, a trade-off between appropriate redundant storage space and efficient data retrieve is achieved. Horizontally, for all levels of the pyramid model, we establish a tiled quadtree index, and generate a cache image for each tile. Secondly, an optimized visualization method in accordance with the storage strategy is also designed. Based on the current area of interest and data dispatch algorithm, we calculate the corresponding tile location and directly load the cache image to lessen the workload of complex spatial data operation, reduce the rendering burden of spatial data. We can generate customized dynamic cache with specific area of interest and scale, to improve the visual effect, too.

Real-time generalization of point data in mobile and web mapping using quadtrees

With a focus on mobile and web mapping, we propose several algorithms for on-the-fly generalization of point data, such as points of interest (POIs) or large point collections. In order to achieve real-time performance, we use a quadtree data structure. With their hierarchical subdivision structure and progressive levels of detail, indices of the quadtree family lend themselves as auxiliary data structures to support algorithms for generalization operations, including selection, simplification, aggregation, and displacement of point data. The spatial index can further be used to generate several local and global measures that can then serve to make educated guesses on the density and proximity of points across map scales, and thus enable control of the operation of the generalization algorithms. An implementation of the proposed algorithms has shown that, and thanks to the quadtree index, real-time performance can be achieved even for large point sets. Furthermore, the quadtree data structure can be extended into a caching structure, which can be used to store pre-computed generalizations; thus, a desired level of detail (LOD) can simply be retrieved from cache.