With the rapid development of information technology,smart teaching platforms have become important tools for higher education teaching reform.As a core course of computer science and technology-related majors in high...With the rapid development of information technology,smart teaching platforms have become important tools for higher education teaching reform.As a core course of computer science and technology-related majors in higher education,the data structure course lays a solid foundation for students’professional learning and plays an important role in promoting their future success in technology,research,and industry.This study conducts an in-depth analysis of the pain points faced by the data structure course,and explores a teaching reform and practice of integration of theory and practice based on the system application of a smart teaching platform before class,during class,and after class.The reform practice shows that this teaching mode improves students’learning initiative,learning motivation,and practical skills.Students not only achieved better results in knowledge mastery but also significantly improved in problem analysis and solution.展开更多
In this paper, a new concept called numerical structure of seismic data is introduced and the difference between numerical structure and numerical value of seismic data is explained. Our study shows that the numerical...In this paper, a new concept called numerical structure of seismic data is introduced and the difference between numerical structure and numerical value of seismic data is explained. Our study shows that the numerical seismic structure is closely related to oil and gas-bearing reservoir, so it is very useful for a geologist or a geophysicist to precisely interpret the oil-bearing layers from the seismic data. This technology can be applied to any exploration or production stage. The new method has been tested on a series of exploratory or development wells and proved to be reliable in China. Hydrocarbon-detection with this new method for 39 exploration wells on 25 structures indi- cates a success ratio of over 80 percent. The new method of hydrocarbon prediction can be applied for: (1) depositional environment of reservoirs with marine fades, delta, or non-marine fades (including fluvial facies, lacustrine fades); (2) sedimentary rocks of reservoirs that are non-marine clastic rocks and carbonate rock; and (3) burial depths range from 300 m to 7000 m, and the minimum thickness of these reservoirs is over 8 m (main frequency is about 50 Hz).展开更多
Seismic data structure characteristics means the waveform character arranged in the time sequence at discrete data points in each 2-D or 3-D seismic trace. Hydrocarbon prediction using seismic data structure character...Seismic data structure characteristics means the waveform character arranged in the time sequence at discrete data points in each 2-D or 3-D seismic trace. Hydrocarbon prediction using seismic data structure characteristics is a new reservoir prediction technique. When the main pay interval is in carbonate fracture and fissure-cavern type reservoirs with very strong inhomogeneity, there are some difficulties with hydrocarbon prediction. Because of the special geological conditions of the eighth zone in the Tahe oil field, we apply seismic data structure characteristics to hydrocarbon prediction for the Ordovician reservoir in this zone. We divide the area oil zone into favorable and unfavorable blocks. Eighteen well locations were proposed in the favorable oil block, drilled, and recovered higher output of oil and gas.展开更多
In order to use data information in the Internet, it is necessary to extract data from web pages. An HTT tree model representing HTML pages is presented. Based on the HTT model, a wrapper generation algorithm AGW is p...In order to use data information in the Internet, it is necessary to extract data from web pages. An HTT tree model representing HTML pages is presented. Based on the HTT model, a wrapper generation algorithm AGW is proposed. The AGW algorithm utilizes comparing and correcting technique to generate the wrapper with the native characteristic of the HTT tree structure. The AGW algorithm can not only generate the wrapper automatically, but also rebuild the data schema easily and reduce the complexity of the computing.展开更多
A robust and efficient algorithm is presented to build multiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge c...A robust and efficient algorithm is presented to build multiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.展开更多
Data protection in databases is critical for any organization,as unauthorized access or manipulation can have severe negative consequences.Intrusion detection systems are essential for keeping databases secure.Advance...Data protection in databases is critical for any organization,as unauthorized access or manipulation can have severe negative consequences.Intrusion detection systems are essential for keeping databases secure.Advancements in technology will lead to significant changes in the medical field,improving healthcare services through real-time information sharing.However,reliability and consistency still need to be solved.Safeguards against cyber-attacks are necessary due to the risk of unauthorized access to sensitive information and potential data corruption.Dis-ruptions to data items can propagate throughout the database,making it crucial to reverse fraudulent transactions without delay,especially in the healthcare industry,where real-time data access is vital.This research presents a role-based access control architecture for an anomaly detection technique.Additionally,the Structured Query Language(SQL)queries are stored in a new data structure called Pentaplet.These pentaplets allow us to maintain the correlation between SQL statements within the same transaction by employing the transaction-log entry information,thereby increasing detection accuracy,particularly for individuals within the company exhibiting unusual behavior.To identify anomalous queries,this system employs a supervised machine learning technique called Support Vector Machine(SVM).According to experimental findings,the proposed model performed well in terms of detection accuracy,achieving 99.92%through SVM with One Hot Encoding and Principal Component Analysis(PCA).展开更多
Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for th...Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.展开更多
The key to develop 3-D GISs is the study on 3-D data model and data structure. Some of the data models and data structures have been presented by scholars. Because of the complexity of 3-D spatial phenomenon, there ar...The key to develop 3-D GISs is the study on 3-D data model and data structure. Some of the data models and data structures have been presented by scholars. Because of the complexity of 3-D spatial phenomenon, there are no perfect data structures that can describe all spatial entities. Every data structure has its own advantages and disadvantages. It is difficult to design a single data structure to meet different needs. The important subject in the3-D data models is developing a data model that has integrated vector and raster data structures. A special 3-D spatial data model based on distributing features of spatial entities should be designed. We took the geological exploration engineering as the research background and designed an integrated data model whose data structures integrats vector and raster data byadopting object-oriented technique. Research achievements are presented in this paper.展开更多
3D GISs were developed simultaneously in the late 1980s in a number of different disciplines.The development of these 3D GISs can not yet meet all needs for new representations and analytical tool s in 3D envir onment...3D GISs were developed simultaneously in the late 1980s in a number of different disciplines.The development of these 3D GISs can not yet meet all needs for new representations and analytical tool s in 3D envir onments.In this paper,the data structures,especially solid-based data representa tions are introduced.Then,a typical object-oriented data model is put forth to s how a new data model.And at last,two data access methods are proposed to make th e data model clear.展开更多
This paper discribes the importance and necessity of the study on the data structures for displaying the mining field using the interactive technology in open pit design and planning,based upon the grid block model. T...This paper discribes the importance and necessity of the study on the data structures for displaying the mining field using the interactive technology in open pit design and planning,based upon the grid block model. The commonly used data structures--rectangular array structure and quadtree structure ,are analyzed. Two compressed data structures--compressed circular link array structure and compressed doubly-linked circular array structure,are proposed,which are much more suitable for displaying the regularly gridded block model. When the two compressed data structures are adopted,the storage space can be tremendously saved and the algorithms are simple,while the requirements of the accuracy and the manipulating speed will be both satisfied for the interactive open pit short range plan formulation.展开更多
. In this article, we describe the characteristics of large-scale modeling of the theme text of this site data and important progress in recent years. Topic modeling approach has attracted wide interest in the world, .... In this article, we describe the characteristics of large-scale modeling of the theme text of this site data and important progress in recent years. Topic modeling approach has attracted wide interest in the world, and promote a number of important data mining, development of computer vision and computational biology applications, including automatic text summaries, information retrieval, information recommendation, topic detection and tracking, natural scene understanding human action recognition and gene expression analysis. The main features of the model and the corresponding theme paper focuses on the text of this site data. Data with dynamic, high-end, multi-channel and distributed structure and the structure of the model is only part of the theme before modeling. The paper discussed in the framework of the unity of the three-dimensional Markov model of four structural features of the text of this site data modeling, and analysis of distributed computing and word combination of three-dimensional modeling topics Markov model and type fuzzy systems the possibility of applications. In addition to structural modeling for this site text data, also we discuss some of the three-dimensional Markov model energy minimization of machine learning algorithms.展开更多
To capitalize on the primary role of major course teaching and to facilitate students’understanding of abstract concepts in the data structure course,it is essential to increase their interest in learning and develop...To capitalize on the primary role of major course teaching and to facilitate students’understanding of abstract concepts in the data structure course,it is essential to increase their interest in learning and develop case studies that highlight fine traditional culture.By incorporating these culture-rich case studies into classroom instruction,we employ a project-driven teaching approach.This not only allows students to master professional knowledge,but also enhances their abilities to solve specific engineering problems,ultimately fostering cultural confidence.Over the past few years,during which educational reforms have been conducted for trial runs,the feasibility and effectiveness of these reform schemes have been demonstrated.展开更多
For the course of“Data Structures”,this paper introduces the importance and existing problems of the data structure course.Through the literature and the current teaching in major universities,the existing teaching ...For the course of“Data Structures”,this paper introduces the importance and existing problems of the data structure course.Through the literature and the current teaching in major universities,the existing teaching methods and their disadvantages are analyzed.The authors put forward teaching reform suggestions and designed an online course platform.展开更多
This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalabil...This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalability by using hierarchical representa-tions of topological elements. The proposed data structure is array-based, and it is a compact representation of the half-edge data structure for volume elements and half-face data structure for volumetric meshes. This guarantees constant access time to the neighbors of the topological elements. In addition, an open-source implementation named Open Volumetric Mesh （OVM） of the pro-posed data structure is written in C＋＋ using generic programming concepts.展开更多
The designing,encodings and an instance of simulation of a binary tree for DNA computer were proposed,which utilizes the method of biology to complete inserting and deleting of the binary tree. Firstly,DNA encodings f...The designing,encodings and an instance of simulation of a binary tree for DNA computer were proposed,which utilizes the method of biology to complete inserting and deleting of the binary tree. Firstly,DNA encodings for storage and all elements of the binary tree were completely given out. Then, the implementations of all bio-operations in DNA computer were described. Finally, to prove the feasibility of this method, an actual binary tree with detailed nucleotide encodings was introduced. The process of an algorithm implemented on this binary tree was demonstrated. Based on this method, more other data structures in DNA computer can be developed.展开更多
This paper describes the nearest neighbor (NN) search algorithm on the GBD(generalized BD) tree. The GBD tree is a spatial data structure suitable for two-or three-dimensional data and has good performance characteris...This paper describes the nearest neighbor (NN) search algorithm on the GBD(generalized BD) tree. The GBD tree is a spatial data structure suitable for two-or three-dimensional data and has good performance characteristics with respect to the dynamic data environment. On GIS and CAD systems, the R-tree and its successors have been used. In addition, the NN search algorithm is also proposed in an attempt to obtain good performance from the R-tree. On the other hand, the GBD tree is superior to the R-tree with respect to exact match retrieval, because the GBD tree has auxiliary data that uniquely determines the position of the object in the structure. The proposed NN search algorithm depends on the property of the GBD tree described above. The NN search algorithm on the GBD tree was studied and the performance thereof was evaluated through experiments.展开更多
In the engineering database system, multiple versions of a design including engineering drawings should be managed efficiently. The paper proposes an efficient spatial data structure, that is an expansion of the R tre...In the engineering database system, multiple versions of a design including engineering drawings should be managed efficiently. The paper proposes an efficient spatial data structure, that is an expansion of the R tree and HR tree, for version management of engineering drawings. A novel mechanism to manage the difference between drawings is introduced to the HR tree to eliminate redundant duplications and to reduce the amount of storage required for the data structure. Data management mechanism and structural properties of our data structure called the MVR + tree are described.展开更多
文摘With the rapid development of information technology,smart teaching platforms have become important tools for higher education teaching reform.As a core course of computer science and technology-related majors in higher education,the data structure course lays a solid foundation for students’professional learning and plays an important role in promoting their future success in technology,research,and industry.This study conducts an in-depth analysis of the pain points faced by the data structure course,and explores a teaching reform and practice of integration of theory and practice based on the system application of a smart teaching platform before class,during class,and after class.The reform practice shows that this teaching mode improves students’learning initiative,learning motivation,and practical skills.Students not only achieved better results in knowledge mastery but also significantly improved in problem analysis and solution.
基金Mainly presented at the 6-th international meeting of acoustics in Aug. 2003, and The 1999 SPE Asia Pacific Oil and GasConference and Exhibition held in Jakarta, Indonesia, 20-22 April 1999, SPE 54274.
文摘In this paper, a new concept called numerical structure of seismic data is introduced and the difference between numerical structure and numerical value of seismic data is explained. Our study shows that the numerical seismic structure is closely related to oil and gas-bearing reservoir, so it is very useful for a geologist or a geophysicist to precisely interpret the oil-bearing layers from the seismic data. This technology can be applied to any exploration or production stage. The new method has been tested on a series of exploratory or development wells and proved to be reliable in China. Hydrocarbon-detection with this new method for 39 exploration wells on 25 structures indi- cates a success ratio of over 80 percent. The new method of hydrocarbon prediction can be applied for: (1) depositional environment of reservoirs with marine fades, delta, or non-marine fades (including fluvial facies, lacustrine fades); (2) sedimentary rocks of reservoirs that are non-marine clastic rocks and carbonate rock; and (3) burial depths range from 300 m to 7000 m, and the minimum thickness of these reservoirs is over 8 m (main frequency is about 50 Hz).
基金This reservoir research is sponsored by the National 973 Subject Project (No. 2001CB209).
文摘Seismic data structure characteristics means the waveform character arranged in the time sequence at discrete data points in each 2-D or 3-D seismic trace. Hydrocarbon prediction using seismic data structure characteristics is a new reservoir prediction technique. When the main pay interval is in carbonate fracture and fissure-cavern type reservoirs with very strong inhomogeneity, there are some difficulties with hydrocarbon prediction. Because of the special geological conditions of the eighth zone in the Tahe oil field, we apply seismic data structure characteristics to hydrocarbon prediction for the Ordovician reservoir in this zone. We divide the area oil zone into favorable and unfavorable blocks. Eighteen well locations were proposed in the favorable oil block, drilled, and recovered higher output of oil and gas.
基金the National Grand Fundamental Research 973 Program of China(G1998030414)
文摘In order to use data information in the Internet, it is necessary to extract data from web pages. An HTT tree model representing HTML pages is presented. Based on the HTT model, a wrapper generation algorithm AGW is proposed. The AGW algorithm utilizes comparing and correcting technique to generate the wrapper with the native characteristic of the HTT tree structure. The AGW algorithm can not only generate the wrapper automatically, but also rebuild the data schema easily and reduce the complexity of the computing.
文摘A robust and efficient algorithm is presented to build multiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.
基金thankful to the Dean of Scientific Research at Najran University for funding this work under the Research Groups Funding Program,Grant Code(NU/RG/SERC/12/6).
文摘Data protection in databases is critical for any organization,as unauthorized access or manipulation can have severe negative consequences.Intrusion detection systems are essential for keeping databases secure.Advancements in technology will lead to significant changes in the medical field,improving healthcare services through real-time information sharing.However,reliability and consistency still need to be solved.Safeguards against cyber-attacks are necessary due to the risk of unauthorized access to sensitive information and potential data corruption.Dis-ruptions to data items can propagate throughout the database,making it crucial to reverse fraudulent transactions without delay,especially in the healthcare industry,where real-time data access is vital.This research presents a role-based access control architecture for an anomaly detection technique.Additionally,the Structured Query Language(SQL)queries are stored in a new data structure called Pentaplet.These pentaplets allow us to maintain the correlation between SQL statements within the same transaction by employing the transaction-log entry information,thereby increasing detection accuracy,particularly for individuals within the company exhibiting unusual behavior.To identify anomalous queries,this system employs a supervised machine learning technique called Support Vector Machine(SVM).According to experimental findings,the proposed model performed well in terms of detection accuracy,achieving 99.92%through SVM with One Hot Encoding and Principal Component Analysis(PCA).
基金Supported by the National Natural Science Foundation of China(21576240)Experimental Technology Research Program of China University of Geosciences(Key Program)(SJ-201422)
文摘Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.
基金Project supported by the National Outstanding Youth Researchers Foundation (No.49525101)the Opening Research Foundation from LIESMARS(WKL(96)0302)
文摘The key to develop 3-D GISs is the study on 3-D data model and data structure. Some of the data models and data structures have been presented by scholars. Because of the complexity of 3-D spatial phenomenon, there are no perfect data structures that can describe all spatial entities. Every data structure has its own advantages and disadvantages. It is difficult to design a single data structure to meet different needs. The important subject in the3-D data models is developing a data model that has integrated vector and raster data structures. A special 3-D spatial data model based on distributing features of spatial entities should be designed. We took the geological exploration engineering as the research background and designed an integrated data model whose data structures integrats vector and raster data byadopting object-oriented technique. Research achievements are presented in this paper.
文摘3D GISs were developed simultaneously in the late 1980s in a number of different disciplines.The development of these 3D GISs can not yet meet all needs for new representations and analytical tool s in 3D envir onments.In this paper,the data structures,especially solid-based data representa tions are introduced.Then,a typical object-oriented data model is put forth to s how a new data model.And at last,two data access methods are proposed to make th e data model clear.
文摘This paper discribes the importance and necessity of the study on the data structures for displaying the mining field using the interactive technology in open pit design and planning,based upon the grid block model. The commonly used data structures--rectangular array structure and quadtree structure ,are analyzed. Two compressed data structures--compressed circular link array structure and compressed doubly-linked circular array structure,are proposed,which are much more suitable for displaying the regularly gridded block model. When the two compressed data structures are adopted,the storage space can be tremendously saved and the algorithms are simple,while the requirements of the accuracy and the manipulating speed will be both satisfied for the interactive open pit short range plan formulation.
文摘. In this article, we describe the characteristics of large-scale modeling of the theme text of this site data and important progress in recent years. Topic modeling approach has attracted wide interest in the world, and promote a number of important data mining, development of computer vision and computational biology applications, including automatic text summaries, information retrieval, information recommendation, topic detection and tracking, natural scene understanding human action recognition and gene expression analysis. The main features of the model and the corresponding theme paper focuses on the text of this site data. Data with dynamic, high-end, multi-channel and distributed structure and the structure of the model is only part of the theme before modeling. The paper discussed in the framework of the unity of the three-dimensional Markov model of four structural features of the text of this site data modeling, and analysis of distributed computing and word combination of three-dimensional modeling topics Markov model and type fuzzy systems the possibility of applications. In addition to structural modeling for this site text data, also we discuss some of the three-dimensional Markov model energy minimization of machine learning algorithms.
基金the research outcomes of a blended top-tier undergraduate course in Henan ProvinceData Structures and Algorithms(Jiao Gao[2022]324)a research-based teaching demonstration course in Henan Province-Data Structures and Algorithms(Jiao Gao[2023]36)a model course of ideological and political education of Anyang Normal University-Data Structures and Algorithms(No.YBKC20210012)。
文摘To capitalize on the primary role of major course teaching and to facilitate students’understanding of abstract concepts in the data structure course,it is essential to increase their interest in learning and develop case studies that highlight fine traditional culture.By incorporating these culture-rich case studies into classroom instruction,we employ a project-driven teaching approach.This not only allows students to master professional knowledge,but also enhances their abilities to solve specific engineering problems,ultimately fostering cultural confidence.Over the past few years,during which educational reforms have been conducted for trial runs,the feasibility and effectiveness of these reform schemes have been demonstrated.
基金supported in part by grants from Qinglan Project of Jiangsu Province(2020)High-level demonstration construction project of Sino-foreign cooperation in running schools in Jiangsu Province,Jiangsu Higher Educational Technology Research Association-2019 Higher Education Informatization Research Project(2019JSETKT035)Ideological and Political Special Project of Philosophy and Social Science Research Projects in Colleges and Universities in 2019(2019SJB422).
文摘For the course of“Data Structures”,this paper introduces the importance and existing problems of the data structure course.Through the literature and the current teaching in major universities,the existing teaching methods and their disadvantages are analyzed.The authors put forward teaching reform suggestions and designed an online course platform.
基金Supported by Fundamental Research Funds for the Central Universities(Nos.2013ZM087,2012zz0062,2012zz0063)Doctoral Fund of Ministry of Education of China(No.20130172120010)
文摘This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalability by using hierarchical representa-tions of topological elements. The proposed data structure is array-based, and it is a compact representation of the half-edge data structure for volume elements and half-face data structure for volumetric meshes. This guarantees constant access time to the neighbors of the topological elements. In addition, an open-source implementation named Open Volumetric Mesh （OVM） of the pro-posed data structure is written in C＋＋ using generic programming concepts.
文摘The designing,encodings and an instance of simulation of a binary tree for DNA computer were proposed,which utilizes the method of biology to complete inserting and deleting of the binary tree. Firstly,DNA encodings for storage and all elements of the binary tree were completely given out. Then, the implementations of all bio-operations in DNA computer were described. Finally, to prove the feasibility of this method, an actual binary tree with detailed nucleotide encodings was introduced. The process of an algorithm implemented on this binary tree was demonstrated. Based on this method, more other data structures in DNA computer can be developed.
文摘This paper describes the nearest neighbor (NN) search algorithm on the GBD(generalized BD) tree. The GBD tree is a spatial data structure suitable for two-or three-dimensional data and has good performance characteristics with respect to the dynamic data environment. On GIS and CAD systems, the R-tree and its successors have been used. In addition, the NN search algorithm is also proposed in an attempt to obtain good performance from the R-tree. On the other hand, the GBD tree is superior to the R-tree with respect to exact match retrieval, because the GBD tree has auxiliary data that uniquely determines the position of the object in the structure. The proposed NN search algorithm depends on the property of the GBD tree described above. The NN search algorithm on the GBD tree was studied and the performance thereof was evaluated through experiments.
文摘In the engineering database system, multiple versions of a design including engineering drawings should be managed efficiently. The paper proposes an efficient spatial data structure, that is an expansion of the R tree and HR tree, for version management of engineering drawings. A novel mechanism to manage the difference between drawings is introduced to the HR tree to eliminate redundant duplications and to reduce the amount of storage required for the data structure. Data management mechanism and structural properties of our data structure called the MVR + tree are described.
