R-tree Structure Research Articles

SGIR-Tree: Integrating R-Tree Spatial Indexing as Subgraphs in Graph Database Management Systems

Efficient spatial query processing in Graph Database Management Systems (GDBMSs) has become increasingly important owing to the prevalence of spatial graph data. However, current GDBMSs lack effective spatial indexing, causing performance issues with complex spatial graph queries. This study proposes a spatial index called Subgraph Integrated R-Tree (SGIR-Tree) for efficient spatial query processing in GDBMSs. The SGIR-Tree integrates the hierarchical R-Tree structure with the graph structure of GDBMSs by converting R-Tree elements into graph components like nodes and edges. The Minimum Bounding Rectangle (MBR) information of spatial objects and R-Tree nodes is stored as properties of these graph elements, and the leaf nodes are directly connected to the spatial nodes. This approach combines the efficiency of spatial indexing with the flexibility of graph databases, thereby allowing spatial query results to be directly utilized in graph traversal. Experiments using OpenStreetMap datasets demonstrate that the SGIR-Tree outperforms the previous approaches in terms of query overhead and index overhead. The results are expected to improve spatial graph data processing in various fields, including location-based service and urban planning, significantly advancing spatial data management in GDBMSs.

A Robust Newton Iteration Method for Mixed-Cell-Height Circuit Legalization Under Technology and Region Constraints

The evolution of advanced technology nodes has prompted a shift toward mixed-cell-height circuit design, while the introduction of technology and fence region constraints further increases the complexity of placement. In this article, we innovatively transform the mixed-cell-height circuit legalization problem into a generalized absolute value equation (GAVE) and propose a novel and effective robust Newton (RN) iteration method to address the challenge of the legalization problem. 1 First, the window-based cell insertion technique is applied to obtain the initial cell row allocation and cell order, and the cells are allocated to the matching region based on the R-tree structure. Then, the legalization problem of cells within the region is transformed into a GAVE, and an RN iteration method is proposed to solve the GAVE. Finally, the maximum displacement cells and technology violation cells are optimized based on a greedy method. Experimental results confirm the efficiency and robustness of the proposed method compared with the state-of-the-art methods.

АНАЛІЗ АЛГОРИТМІВ ВИЯВЛЕННЯ ЗІТКНЕНЬ У ТРИВИМІРНИХ ВІРТУАЛЬНИХ СЕРЕДОВИЩАХ

The problem addressed in this paper concerns the real-time detection of collisions in virtual environments, which can consume a significant portion of computational re-sources, particularly in complex simulations with numerous objects. Ensuring a minimum frame rate of 30 FPS is crucial for user-friendly simulations. The focus is on the narrow phase of collision detection, where objects in close proximity are examined for potential collisions. This paper proposes a collision detection algorithm leveraging Directed Bounding Parallels (AABB) R-tree structure and Oriented Bounding Parallelepiped Inter-section (OAABB) method to address this phase efficiently. Experimental results demon-strate the effectiveness of the algorithm in detecting intersections with high interaction rates. Various publicly available toolkits exist for narrow phase collision detection, em-ploying different bounding volume hierarchies and constraint volumes. Comparing these approaches is challenging due to performance variations influenced by factors such as object shapes, contact types, and model sizes. Nonetheless, these algorithms are crucial for accurately detecting collisions in virtual environments and gaming applications. Bounding Volume Hierarchies (BVH), commonly used for collision detection, organ-ize object geometry and improve performance by reducing test pair numbers through vol-ume constraints. The proposed algorithm utilizes R-tree hierarchies of directed bounding parallelepipeds and OAABB to enhance collision detection efficiency by minimizing up-date and intersect operations. The choice of constraint volume type impacts collision de-tection performance, with oriented parallelepipeds offering faster intersections. To expedite collision detection, each feature is represented by an R-tree data struc-ture in its local coordinate system. Hierarchical trees are constructed by grouping adja-cent surfaces, with leaves indicating surface geometry. Additionally, R-trees are em-ployed to spatially organize triangles within surfaces to quickly discard non-intersecting triangles. The algorithm leverages OAABB, a concept involving the common volume between two oriented bounding parallelepipeds, to filter out primitives that cannot intersect. Tra-versal algorithms are utilized to reduce the number of node visits, addressing inefficien-cies observed in traditional schemes. OAABB contributes significantly to reducing volume refresh operations. Experimental evaluations demonstrate the proposed algorithm's efficacy in real-world industrial applications, achieving interactive performance. Comparisons with al-ternative methods highlight the algorithm's effectiveness in collision detection. Overall, the proposed approach offers a robust solution to the narrow phase collision detection problem in virtual environments.

The RLR-Tree: A Reinforcement Learning Based R-Tree for Spatial Data

Learned indexes have been proposed to replace classic index structures like B-Tree with machine learning (ML) models. They require to replace both the indexes and query processing algorithms currently deployed by the databases, and such a radical departure is likely to encounter challenges and obstacles. In contrast, we propose a fundamentally different way of using ML techniques to build a better R-Tree without the need to change the structure or query processing algorithms of traditional R-Tree. Specifically, we develop reinforcement learning (RL) based models to decide how to choose a subtree for insertion and how to split a node when building and updating an R-Tree, instead of relying on hand-crafted heuristic rules currently used by the R-Tree and its variants. Experiments on real and synthetic datasets with up to more than 100 million spatial objects show that our RL based index outperforms the R-Tree and its variants in terms of query processing time.

Optimization Method of Spatial Layout of Marine Industry Based on Cloud Computing

With the continuous expansion of the marine economy, a large number of problems have been encountered in the spatial layout of the marine industry, such as space intensification, low space utilization, unreasonable industrial structure, poor management system, inadequate scientific research and innovation capabilities, poor ecological environment, poor load balance, and large resource consumption, etc. In response to these problems, this study proposes to reoptimize the spatial layout of the marine industry on the basis of cloud computing. On the basis of collecting the Hilbert values of all data, all nodes are arranged in the order of construction time to improve the Hilbert R-tree structure. Then the idea of clustering is introduced to avoid data overlap. Using the spatial correlation coefficient, the access control model of the marine industry spatial layout platform is established to optimize the marine industry spatial layout under the background of cloud computing. When using the method proposed in this study, the time consumption was about 4 seconds when the number of blocks increased to 5000. Compared with 11 seconds and 7 seconds when using the other two methods, the proposed method greatly reduces the time consumed by the number of pieces of ocean remote sensing images in different query ranges under the ocean information cloud platform. The proposed method also shows good performance in the encryption and decryption test process of the pairing method. In summary, the feasibility and effectiveness of the proposed method in the optimization of the marine industry spatial layout is confirmed, which provides a suitable theoretical basis for the optimization of the marine industry spatial layout.

Secure Semantic-Aware Search Over Dynamic Spatial Data in VANETs

Vehicular Ad hoc Networks (VANETs) play an increasingly important role in a number of applications, particularly those associated with location-based services (e.g., spatial keyword searches – SKS). However, there is a need to strike a balance between privacy guarantee and search efficiency, and existing SKS solutions cannot be directly implemented in VANETs. In addition, existing schemes may also lack support for semantic-awareness in the dynamic setting. To address these limitations, we propose a Secure Semantic-aware Spatial Keyword Search scheme that supports Dynamic update (3SKSD). Specifically, we leverage the Latent Dirichlet Allocation (LDA) topic model and secure <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> Nearest Neighbor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> NN) method to help us achieve both efficiency and security. We also construct an encrypted R-tree structure to facilitate SKS and dynamic update. Moreover, we propose an advanced scheme with forward security on the basis of 3SKSD, with the aim of minimizing privacy leakage due to dynamic updates. Our formal security analysis verifies the validity and security of 3SKSD, and findings from the experimental evaluation demonstrate its high search accuracy and efficiency.

Riso-Tree: An Efficient and Scalable Index for Spatial Entities in Graph Database Management Systems

With the ubiquity of spatial data, vertexes or edges in graphs can possess spatial location attributes side by side with other non-spatial attributes. For instance, as of June 2018, the Wikidata knowledge graph contains 48,547,142 data items (i.e., vertexes) and 13% of them have spatial location attributes. The article proposes Riso-Tree, a generic efficient and scalable indexing framework for spatial entities in graph database management systems. Riso-Tree enables the fast execution of graph queries that involve different types of spatial predicates (GraSp queries). The proposed framework augments the classic R-Tree structure with pre-materialized sub-graph entries. The pruning power of R-Tree is enhanced with the sub-graph information. Riso-Tree partitions the graph into sub-graphs based on their connectivity to the spatial sub-regions. The proposed index allows for the fast execution of GraSp queries by efficiently pruning the traversed vertexes/edges based upon the materialized sub-graph information. The experiments show that the proposed Riso-Tree achieves up to two orders of magnitude faster execution time than its counterparts when executing GraSp queries on real graphs (e.g., Wikidata). The strategy of limiting the size of each sub-graph entry ( PN max ) is proposed to reduce the storage overhead of Riso-Tree. The strategy can save up to around 70% storage without harming the query performance according to the experiments. Another strategy is proposed to ensure the performance of the index maintenance (Irrelevant Vertexes Skipping). The experiments show that the strategy can improve performance, especially for slow updates. It proves that Riso-Tree is useful for applications that need to support frequent updates.

R-tree data structure implementation for Computer Aided Engineering (CAE) tools

Searching and handling geometric data are basic requirements of any Computer Aided Engineering application (CAE). Spatial search and local search has greater importance in CAD and CAE applications for reducing the model preparation time. There are many efficient algorithms being made to search geometrical data. Current neighbour search strategy is limited and not efficient in different CAE platforms. R-tree is tree data structure used for spatial access methods. This paper presents a review of R-tree data structure with its implementation in one of the CAE tool for neighbour search and local search. It satisfies current neighbour search requirements in CAE tools. Results shows considerable amount of time saving compared to the conventional approach. This work concludes that R-tree implementation can be helpful in identifying neighbour part and reducing model preparation time in CAD and CAE tools.

Event detection in educational records: An application of big data approaches

As the exponential growth of predictive analytics applied to educational institutions continues, with various goals in mind, an event detection system could serve as the foundation for more sophisticated predictive systems. What is envisioned is a system that flags educational records that have a sudden change (i.e., event detection in education records). The basic algorithm prosed would retrieve the current week's data for each student, calculate Euclidian and Mahalanobis distances among current week's data, and historical student data, sort all student data based on these distances, and update historical data with current data. The educational event detection system uses a query-based, R-tree structure, big data analytical approach. A simulated experiment determined that the event detection algorithm was able to detect relatively small changes in simulated data. Although, the units of the two distance metrics do not coincide, so distance measurements are not directly comparable, the event detection algorithm with the two different distance metrics have comparable CPU run times. Research and suggestions for constructing predictive analytics on student learners' attrition/retention approaches were documented.

LAZY R-tree: The R-tree with lazy splitting algorithm

The spatial index is a data structure formed according to the position and shape of the spatial object or the relationship between the spatial objects according to certain rules, and the spatial data is managed by an effective spatial data structure. The quality of a spatial index directly affects the performance of spatial queries. The R-tree index structure is a highly efficient spatial index. According to the R-tree query rule, when performing spatial query, most data that is not related to the query condition can be filtered out, and finally, a few leaf nodes can be accessed to query the data satisfying the condition. Its query performance is affected by factors such as non-leaf node overlap and node space utilisation. This article proposes a lazy splitting method to improve the R-tree construction process. The scheme works as follows: (1) When a node overflows, it creates an overflow node for that node and all overflow nodes are saved in a hash table. (2) If the node continues to insert data, the data are added to its overflow node. (3) When an overflow node is saturated, the node and its overflow node are split into two saturated nodes. We use both simulated and actual data to perform experiments. The experimental results show that an R-tree constructed by the lazy algorithm is superior to an R-tree constructed using the original R-tree PM algorithm or the corner-based splitting (CBS) algorithm based on the number of splits created, the node space used and the efficiency of region queries and k-nearest neighbour (kNN) queries.

SRC

Graph has become a powerful tool to model real life data. There are companies building their products based on graph data model, such as Facebook and LinkedIn. Moreover, thanks to location-aware devices, spatial data can be collected quickly with cheap price and spatial-aware services are popular in our daily lives, such as Google Map. GeoSocial graph integrates social graph model with spatial locations, which has already triggered many interesting applications. It also brings the challenges to efficiently searching the spatial graph data. In this paper, we propose an augmented R-Tree structure, Riso-Tree, which can achieve up to 100x better performance than state-of-the-art methods in solving location-based graph queries.

Sensor Information Retrieval From Internet of Things: Representation and Indexing

Billions of devices are connected in the Internet of Things (IoT)-based sensor networks and they continuously generate a large volume of data. In order to get access to specific data, which is crucial to enable a myriad of new intelligent applications, efficient information retrieval becomes an imminent need for IoT. However, sensor information in the physical world can be heterogeneous, high dimensional, and voluminous due to the complex and dynamic environments. In this paper, we first investigate several IoT search scenarios and propose a uniform representation model for sensor information recordings. Four query models are designed to represent all possible information query styles. With these models, we develop information retrieval architecture for IoT. In essence, an indexing mechanism called efficiency maximization and cost minimization is proposed to solve the property selection problem in the process of index construction and update. Meanwhile, a novel real-time grid R-tree structure is designed to support historical and real-time search for spatiotemporal observation data. Simulation results based on real-world IoT data sets show that storage space is considerably reduced with the sensor model. Furthermore, the proposed indexing mechanisms can improve retrieval efficiency and accuracy, and ensure scalability for large-sized data simultaneously.

A MongoDB-Based Management of Planar Spatial Data with a Flattened R-Tree

This paper addresses how to manage planar spatial data using MongoDB, a popular NoSQL database characterized as a document-oriented, rich query language and high availability. The core idea is to flatten a hierarchical R-tree structure into a tabular MongoDB collection, during which R-tree nodes are represented as collection documents and R-tree pointers are expressed as document identifiers. By following this strategy, a storage schema to support R-tree-based create, read, update, and delete (CRUD) operations is designed and a module to manage planar spatial data by consuming and maintaining flattened R-tree structure is developed. The R-tree module is then seamlessly integrated into MongoDB, so that users could manipulate planar spatial data with existing command interfaces oriented to geodetic spatial data. The experimental evaluation, using real-world datasets with diverse coverage, types, and sizes, shows that planar spatial data can be effectively managed by MongoDB with our flattened R-tree and, therefore, the application extent of MongoDB will be greatly enlarged. Our work resulted in a MongoDB branch with R-tree support, which has been released on GitHub for open access.

Towards trajectory anonymisation using multi-dimensional index structures

Trajectory datasets are increasingly available due to the technological advances in location-sensing devices, wireless technologies, and hand-held devices. However, the datasets also causes consumer privacy concerns. This paper addresses the privacy issues by using the internal structure of R-tree, a multi-dimensional index structure. The benefit of using R-tree is that it clusters trajectories in a way that their bounding spatiotemporal extension is minimised, thus achieving better quality in the anonymised database. This is a desirable property of the resulting anonymised database. In order to improve the quality of service requirements, a novel algorithm has been proposed.

Towards trajectory anonymisation using multi-dimensional index structures

Trajectory datasets are increasingly available due to the technological advances in location-sensing devices, wireless technologies, and hand-held devices. However, the datasets also causes consumer privacy concerns. This paper addresses the privacy issues by using the internal structure of R-tree, a multi-dimensional index structure. The benefit of using R-tree is that it clusters trajectories in a way that their bounding spatiotemporal extension is minimised, thus achieving better quality in the anonymised database. This is a desirable property of the resulting anonymised database. In order to improve the quality of service requirements, a novel algorithm has been proposed.

Extended Rice Code and Its application to R-Tree Compression

ABSTRACTCompression techniques are essential for those applications which require more disk accesses. Since the uncompressed data need more disk accesses than the compressed data, compression is used for reducing the costs of disk access to enable the retrieval of data to be faster. Various variable length codes, such as Elias codes, Rice code, and fast extended Golomb code have been used in many applications to compress the data. Particularly, these codes have been used in information retrieval-based applications to compress integers. In these applications, integers are the basis of indexes that are used to resolve queries. This paper has proposed a new method to represent non-negative integers based on the idea used in Rice code and fast extended Golomb code. The variable length codes produced by the proposed method can be suitable for representing small, middle, and large range of integers, where Rice code suits well for representing small or middle or large range of integers. This method also gives better representation for most of the integers from small-to-large range than fast extended Golomb code. In this paper, the proposed method has been applied to compress the coordinates (integers) used in the R-tree structure, which is used for indexing the spatial data. In the experiments, TIGER data collections and synthetic data collections have been used to evaluate the compression performance. The experimental results show that our code achieves better bit-rate than other existing codes for those spatial data files, which contain significant distribution of small, middle, and large integers.

An Effective Probabilistic Skyline Query Process on Uncertain Data Streams

Abstract With the evolution of technology, the ways to acquire data and the applications of data are more diverse. As data volume con- tinuously grows, the data quality may not be high as usual. The data can be defected, imprecise or inaccurate due to the process of data acquiring. Recently, the skyline query is widely used in data analysis to derive the results that meets more than one spe- cific condition simultaneously. For example, the forest monitoring system, which collects the temperature and humidity of the surrounding environment with sensors, to monitor the disasters. Using the skyline query, the zones of potential fire hazards can be found in time, where the temperature is high and the humidity is low. In the mentioned application, the derived data change with time. We refer to such data as data streams. The constant change and uncertainty of data make the query process difficult and need more computations. Thus, how to have an effective skyline query process in terms of time and space over uncertain data streams becomes crucial. In this paper, we discuss this problem and propose an effective approach, Efficient Probabilistic Skyline Update (EPSU), using a new data structure by augmenting the R-tree structure. The relevant algorithms are analyzed and discussed. Last, we perform the simulated experiments extensively with synthetic data to validate the EPSU approach. The results show that EPSU can effectively compute the probabilistic skyline query in terms of the time and space and outperforms the existing ones.

A hybrid spatio-temporal data indexing method for trajectory databases.

In recent years, there has been tremendous growth in the field of indoor and outdoor positioning sensors continuously producing huge volumes of trajectory data that has been used in many fields such as location-based services or location intelligence. Trajectory data is massively increased and semantically complicated, which poses a great challenge on spatio-temporal data indexing. This paper proposes a spatio-temporal data indexing method, named HBSTR-tree, which is a hybrid index structure comprising spatio-temporal R-tree, B*-tree and Hash table. To improve the index generation efficiency, rather than directly inserting trajectory points, we group consecutive trajectory points as nodes according to their spatio-temporal semantics and then insert them into spatio-temporal R-tree as leaf nodes. Hash table is used to manage the latest leaf nodes to reduce the frequency of insertion. A new spatio-temporal interval criterion and a new node-choosing sub-algorithm are also proposed to optimize spatio-temporal R-tree structures. In addition, a B*-tree sub-index of leaf nodes is built to query the trajectories of targeted objects efficiently. Furthermore, a database storage scheme based on a NoSQL-type DBMS is also proposed for the purpose of cloud storage. Experimental results prove that HBSTR-tree outperforms TB*-tree in some aspects such as generation efficiency, query performance and query type.

Event R-Tree Miner: an Efficient Approach to Mine Sequential Patterns from Spatio-Temporal Event Dataset

With the advances of technologies such as GPS, remote sensing, RFID, indoor locating devices, and geosensor networks, mining of spatio-temporal patterns seems more important to track spatio-temporal phenomena with increasingly finer spatial resolutions. Accordingly, we have presented an efficient approach to mine sequential patterns from spatio-temporal event datasets. Here, we make use of three major challenges, such as 1) definition of significance measure for finding spatio-temporal sequential pattern, 2) event tree, to reduce the running time and, 3) the definition of adaptive neighborhood to improve the accuracy. Based on these three challenges, R-tree data structure is utilized to construct the event R-tree for avoiding the accessing of database every time. Furthermore, follow ratio, a significance measure is proposed for finding the significant spatio-temporal sequential patterns and the sequence behavior of spatio-temporal events are identified with the help of adaptive neighborhood that is bounded with MBR condition. Finally, the experimentation is made with the real and synthetic dataset and we have proved the efficiency of the proposed event R-tree miner than the STS miner in terms of computation time

Research on Query Mechanism of Moving Object Database

Since the mobile radio communication in a wireless mobile environment, which inevitably subject to fading and interference effects of the various signals, multipath and time-domain signal to bring the mobile domain and frequency dispersion problems, bandwidth resources restricted and transmission delay increases and so on. In this paper, the use of Class R-Tree data structure to store the data on the basis of historical trajectory, the update query results by the beach line iterative way to solve the problem of nearest neighbor queries efficiently update existing intermediate results.