Multidimensional access methods

Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great variety of multidimensional access methods to support such operations. We give an overview of that work. After a brief survey of spatial data management in general, we first present the class of point access methods, which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results concerning the relative performance of various approaches.

[1]  Markku Tamminen,et al.  The extendible cell method for closest point problems , 1982, BIT.

[2]  Hans-Werner Six,et al.  Twin grid files: space optimizing access schemes , 1988, SIGMOD '88.

[3]  Hans-Peter Kriegel,et al.  Efficient processing of spatial joins using R-trees , 1993, SIGMOD Conference.

[4]  Hans-Werner Six,et al.  The LSD tree: Spatial Access to Multidimensional Point and Nonpoint Objects , 1989, VLDB.

[5]  Witold Litwin,et al.  Linear Hashing: A new Algorithm for Files and Tables Addressing , 1980, ICOD.

[6]  Hans-Peter Kriegel,et al.  The TR*-Tree: A New Representation of Polygonal Objects Supporting Spatial Queries and Operations , 1991, Workshop on Computational Geometry.

[7]  Andreas Henrich,et al.  Extending a Spatial Access Structure to Support Additional Standard Attributes , 1995, SSD.

[8]  Jeffrey F. Naughton,et al.  Generalized Search Trees for Database Systems , 1995, VLDB.

[9]  Jack A. Orenstein.  Spatial query processing in an object-oriented database system , 1986, SIGMOD '86.

[10]  Tiko Kameda,et al.  The R-Link Tree: A Recoverable Index Structure for Spatial Data , 1994, DEXA.

[11]  Henk M. Blanken,et al.  The generalized grid file: description and performance aspects , 1990, [1990] Proceedings. Sixth International Conference on Data Engineering.

[12]  Volker Gaede,et al.  Optimal Redundancy in Spatial Database Systems , 1995, SSD.

[13]  Oliver Günther,et al.  Benchmarking spatial joins a la carte , 1998, Proceedings. Tenth International Conference on Scientific and Statistical Database Management (Cat. No.98TB100243).

[14]  Hans-Peter Kriegel,et al.  The Buddy-Tree: An Efficient and Robust Access Method for Spatial Data Base Systems , 1990, VLDB.

[15]  David B. Lomet,et al.  Access method concurrency with recovery , 1992, SIGMOD '92.

[16]  Bernhard Seeger.  Performance Comparison of Segment Access Methods Implemented on Top of the Buddy-Tree , 1991, SSD.

[17]  Sridhar Ramaswamy,et al.  Indexing for Data Models with Constraints and Classes , 1996, J. Comput. Syst. Sci..

[18]  Timos K. Sellis,et al.  A model for the prediction of R-tree performance , 1996, PODS.

[19]  Oliver Günther,et al.  Oversize Shelves: A Storage Management Technique for Large Spatial Data Objects , 1997, Int. J. Geogr. Inf. Sci..

[20]  Jack A. Orenstein.  Redundancy in spatial databases , 1989, SIGMOD '89.

[21]  Ralf Hartmut Güting,et al.  Rule-based optimization and query processing in an extensible geometric database system , 1992, TODS.

[22]  T. H. Merrett,et al.  A class of data structures for associative searching , 1984, PODS.

[23]  H. V. Jagadish,et al.  On Indexing Line Segments , 1990, VLDB.

[24]  Jon Louis Bentley,et al.  Multidimensional Binary Search Trees in Database Applications , 1979, IEEE Transactions on Software Engineering.

[25]  Per-Åke Larson,et al.  Linear Hashing with Partial Expansions , 1980, VLDB.

[26]  Gershon Kedem.  The Quad-CIF Tree: A Data Structure for Hierarchical On-Line Algorithms , 1982, 19th Design Automation Conference.

[27]  Terence R. Smith,et al.  Design and Implementation of Large Spatial Databases , 1989, Lecture Notes in Computer Science.

[28]  Michael J. Maher,et al.  Separability of polyhedra for optimal filtering of spatial and constraint data , 1995, PODS '95.

[29]  Christian Zimmermann,et al.  Global Order Makes Spatial Access Faster , 1992 .

[30]  Ekow J. Otoo,et al.  A Mapping Function for the Directory of a Multidimensional Extendible Hashing , 1984, VLDB.

[31]  Jürg Nievergelt.  7 ± 2 Criteria for Assessing and Comparing Spatial data Structures , 1989, SSD.

[32]  R. Ng,et al.  Eecient and Eeective Clustering Methods for Spatial Data Mining , 1994 .

[33]  David B. Lomet,et al.  Grow and Post Index Trees: Roles, Techniques and Future Potential , 1991, SSD.

[34]  Oliver Günther,et al.  The design of the cell tree: an object-oriented index structure for geometric databases , 1989, [1989] Proceedings. Fifth International Conference on Data Engineering.

[35]  Ludger Becker,et al.  A New Algorithm and a Cost Model for Join Processing with Grid Files , 1992, GI Datenbank Rundbrief.

[36]  Georgios D. Evangelidis,et al.  The hB II -Tree: A Concurrent And Recoverable Multi-Attribute Index Structure , 1994 .

[37]  Nick Roussopoulos,et al.  Direct spatial search on pictorial databases using packed R-trees , 1985, SIGMOD Conference.

[38]  Mireille Régnier,et al.  Analysis of grid file algorithms , 1985, BIT.

[39]  Hemant K. Bhargava,et al.  MMM: A Web-Based System for Sharing Statistical Computing Modules , 1997, IEEE Internet Comput..

[40]  Christos Faloutsos,et al.  Estimating the Selectivity of Spatial Queries Using the 'Correlation' Fractal Dimension , 1995, VLDB.

[41]  Klaus H. Hinrichs,et al.  Storage and Access Structures for Geometric Data Bases , 1985, FODO.

[42]  Sridhar Ramaswamy,et al.  Indexing for data models with constraints and classes (extended abstract) , 1993, PODS '93.

[43]  Christos Faloutsos,et al.  Parallel R-trees , 1992, SIGMOD '92.

[44]  Hanan Samet,et al.  Benchmarking Spatial Join Operations with Spatial Output , 1995, VLDB.

[45]  Andreas Henrich.  Adapting the Transformation Technique to Maintain Multi-Dimensional Non-Point Objects in k-d-Tree Based Access Structures , 1995, ACM-GIS.

[46]  Hans-Peter Kriegel,et al.  Multi-step processing of spatial joins , 1994, SIGMOD '94.

[47]  Allen Klinger,et al.  PATTERNS AND SEARCH STATISTICS , 1971 .

[48]  Walter A. Burkhard,et al.  Interpolation-based index maintenance , 1983, BIT.

[49]  Hans-Peter Kriegel.  Performance comparison of index structures for multi-key retrieval , 1984, SIGMOD '84.

[50]  Jürg Nievergelt,et al.  The Grid File: An Adaptable, Symmetric Multi-Key File Structure , 1981, ECI.

[51]  Christos Faloutsos,et al.  Analysis of object oriented spatial access methods , 1987, SIGMOD '87.

[52]  Jack A. Orenstein.  A Dynamic Hash File for Random and Sequential Accessing , 1983, VLDB.

[53]  Wolf-Fritz Riekert,et al.  Spatial Access Methods and Query Processing in the Object-Oriented GIS GODOT , 1994, AGDM.

[54]  Oliver G Unther.  Eecient Computation of Spatial Joins , 1993 .

[55]  Max J. Egenhofer,et al.  Spatial SQL: A Query and Presentation Language , 1994, IEEE Trans. Knowl. Data Eng..

[56]  Andrew U. Frank,et al.  The Fieldtree: A Data Structure for Geographic Information Systems , 1990, SSD.

[57]  Diane Greene,et al.  An implementation and performance analysis of spatial data access methods , 1989, [1989] Proceedings. Fifth International Conference on Data Engineering.

[58]  Hans-Peter Kriegel,et al.  Comparison of approximations of complex objects used for approximation-based query processing in spatial database systems , 1993, Proceedings of IEEE 9th International Conference on Data Engineering.

[59]  LandscapesByPeter F. Stadlera.  Towards Theory: , 2021, Philosophy Behind Bars.

[60]  Lee Naish.  Constraint Search Trees , 1997 .

[61]  Timos K. Sellis,et al.  Topological relations in the world of minimum bounding rectangles: a study with R-trees , 1995, SIGMOD '95.

[62]  Chuan-Heng Ang,et al.  New Linear Node Splitting Algorithm for R-trees , 1997, SSD.

[63]  Akhil Kumar.  A Study of Spatial Clustering techniques , 1994, DEXA.

[64]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[65]  Jiawei Han,et al.  Efficient and Effective Clustering Methods for Spatial Data Mining , 1994, VLDB.

[66]  Jon Louis Bentley,et al.  Data Structures for Range Searching , 1979, CSUR.

[67]  David B. Lomet,et al.  The hB-tree: a multiattribute indexing method with good guaranteed performance , 1990, TODS.

[68]  Shashi Shekhar,et al.  CCAM: A Connectivity-Clustered Access Method for Networks and Network Computations , 1997, IEEE Trans. Knowl. Data Eng..

[69]  共立出版株式会社.  コンピュータ・サイエンス : ACM computing surveys , 1978 .

[70]  Oliver Günther.  Efficient Computation of Spatial Joins , 1993, ICDE.

[71]  J. T. Robinson,et al.  The K-D-B-tree: a search structure for large multidimensional dynamic indexes , 1981, SIGMOD '81.

[72]  Paul G. Sorenson,et al.  Improved Partial-Match Search Algorithms for BD Trees , 1991, Comput. J..

[73]  Michael Stonebraker,et al.  Readings in Database Systems , 1988 .

[74]  Hans-Peter Kriegel,et al.  An Access Method Based Query Processor for Spatial Database Systems , 1992 .

[75]  Michael Freeston,et al.  Advances in the Design of the BANG File , 1989, FODO.

[76]  Christos Faloutsos,et al.  Beyond uniformity and independence: analysis of R-trees using the concept of fractal dimension , 1994, PODS.

[77]  Hans-Werner Six,et al.  Globally order preserving multidimensional linear hashing , 1988, Proceedings. Fourth International Conference on Data Engineering.

[78]  Paul G. Sorenson,et al.  Algorithms for BD trees , 1986, Softw. Pract. Exp..

[79]  Calvin C. Gotlieb,et al.  Order-preserving key transformations , 1986, TODS.

[80]  M. W. Forreston.  Advances in the design of the BANG file , 1989 .

[81]  Henry Fuchs,et al.  Near real-time shaded display of rigid objects , 1983, SIGGRAPH.

[82]  Sridhar Ramaswamy,et al.  The P-range tree: a new data structure for range searching in secondary memory , 1995, SODA '95.

[83]  Christos Faloutsos,et al.  Gray Codes for Partial Match and Range Queries , 1988, IEEE Trans. Software Eng..

[84]  Hans-Peter Kriegel,et al.  Multidimensional dynamic quantile hashing is very efficient for non-uniform record distributions , 1987, 1987 IEEE Third International Conference on Data Engineering.

[85]  Hans-Peter Kriegel,et al.  Multidimensional Order Preserving Linear Hashing with Partial Expansions , 1986, ICDT.

[86]  Markku Tamminen.  Comment on Quad- and Octtrees , 1984, CACM.

[87]  Hans-Peter Kriegel,et al.  The Impact of Global Clustering on Spatial Database Systems , 1994, VLDB.

[88]  Arie Shoshani,et al.  Efficient organization and access of multi-dimensional datasets on tertiary storage systems , 1995, Inf. Syst..

[89]  Jürg Nievergelt,et al.  The Grid File: An Adaptable, Symmetric Multikey File Structure , 1984, TODS.

[90]  David M. Mark,et al.  A Comparative Analysis of some 2-Dimensional Orderings , 1990, Int. J. Geogr. Inf. Sci..

[91]  Alfons Kemper,et al.  An analysis of geometric modeling in database systems , 1987, CSUR.

[92]  Ming-Ling Lo,et al.  Spatial joins using seeded trees , 1994, SIGMOD '94.

[93]  Mark Wallace,et al.  An Informal Introduction to Constraint Database Systems , 1997, CDB.

[94]  J. L. Smith,et al.  A data structure and algorithm based on a linear key for a rectangle retrieval problem , 1983, Comput. Vis. Graph. Image Process..

[95]  D. B. Lomet,et al.  A robust multi-attribute search structure , 1989, [1989] Proceedings. Fifth International Conference on Data Engineering.

[96]  Aris M. Ouksel.  The interpolation-based grid file , 1985, PODS '85.

[97]  Peter Widmayer,et al.  Datenstrukturen für Geodatenbanken , 1991, Entwicklungstendenzen bei Datenbanksystemen.

[98]  Michael Freeston.  A general solution of the n-dimensional B-tree problem , 1995, SIGMOD '95.

[99]  Hanan Samet,et al.  Hierarchical representations of collections of small rectangles , 1988, CSUR.

[100]  Christos Faloutsos,et al.  The R+-Tree: A Dynamic Index for Multi-Dimensional Objects , 1987, VLDB.

[101]  Curtis P. Kolovson,et al.  Indexing techniques for multi-dimensional spatial data and historical data in database management systems , 1991 .

[102]  Shashi Shekhar,et al.  CCAM: a connectivity-clustered access method for aggregate queries on transportation networks: a summary of results , 1995, Proceedings of the Eleventh International Conference on Data Engineering.

[103]  Volker Gaede.  Geometric Information Makes Spatial Query Processing More Efficient , 1995, ACM-GIS.

[104]  Thomas Brinkhoff.  Der spatial join in Geo-Datenbanksystemen , 1994 .

[105]  Hans-Werner Six,et al.  Spatial searching in geometric databases , 1988, Proceedings. Fourth International Conference on Data Engineering.

[106]  M. J. van Kreveld,et al.  Maintaining range trees in secondary memory. Part I: Partitions , 1987 .

[107]  H. V. Jagadish,et al.  Linear clustering of objects with multiple attributes , 1990, SIGMOD '90.

[108]  Oliver Günther,et al.  Research issues in spatial databases , 1990, SGMD.

[109]  Nick Koudas,et al.  Filter Trees for Managing Spatial Data over a Range of Size Granularities , 1996, VLDB.

[110]  Michael Stonebraker,et al.  An Analysis of Rule Indexing Implementations in Data Base Systems , 1986, Expert Database Conf..

[111]  Ralf Hartmut Güting,et al.  Gral: An Extensible Relational Database System for Geometric Applications , 1989, VLDB.

[112]  Hanan Samet,et al.  Applications of spatial data structures , 1989 .

[113]  H. V. Jagadish.  Spatial search with polyhedra , 1990, [1990] Proceedings. Sixth International Conference on Data Engineering.

[114]  Beng Chin Ooi,et al.  Efficient Query Processing in Geographic Information Systems , 1990, Lecture Notes in Computer Science.

[115]  Michael Freeston,et al.  The BANG file: A new kind of grid file , 1987, SIGMOD '87.

[116]  S. B. Yao,et al.  Efficient locking for concurrent operations on B-trees , 1981, TODS.

[117]  Hans-Peter Kriegel,et al.  The R*-tree: an efficient and robust access method for points and rectangles , 1990, SIGMOD '90.

[118]  Rudolf Bayer.  The Universal B-Tree for multidimensional Indexing , 1996 .

[119]  Hans-Peter Kriegel,et al.  Performance Comparison of Point and Spatial Access Methods , 1990, SSD.

[120]  Markku Tamminen.  Performance analysis of cell based geometric file organizations , 1983, Comput. Vis. Graph. Image Process..

[121]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[122]  Klaus H. Hinrichs,et al.  Implementation of the grid file: Design concepts and experience , 1985, BIT.

[123]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[124]  Christos Faloutsos,et al.  On packing R-trees , 1993, CIKM '93.

[125]  Marcel Kornacker,et al.  High-Concurrency Locking in R-Trees , 1995, VLDB.

[126]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[127]  Oliver Günther,et al.  Spatial database indices for large extended objects , 1991, [1991] Proceedings. Seventh International Conference on Data Engineering.

[128]  Michael Schiwietz.  Speicherung und Anfragebearbeitung komplexer Geo-Objekte , 1993 .

[129]  Peter J. Stuckey.  Constraint Search Tree , 1997, ICLP.

[130]  Aris M. Ouksel,et al.  Storage mappings for multidimensional linear dynamic hashing , 1983, PODS.

[131]  Oliver Günther,et al.  Efficient Structures for Geometric Data Management , 1988, Lecture Notes in Computer Science.

[132]  Christos Faloutsos,et al.  Analysis of n-Dimensional Quadtrees using the Hausdorff Fractal Dimension , 1996, VLDB.

[133]  Ronald Fagin,et al.  Extendible hashing—a fast access method for dynamic files , 1979, ACM Trans. Database Syst..

[134]  Hans-Peter Kriegel,et al.  The X-tree : An Index Structure for High-Dimensional Data , 2001, VLDB.

[135]  Peter Widmayer,et al.  The LSD tree: spatial access to multidimensional and non-point objects , 1989, VLDB 1989.

[136]  Oliver Günther.  Evaluation of Spatial Access Methods with Oversize Shelves , 1992 .

[137]  Walter A. Burkhard,et al.  Index maintenance for non-uniform record distributions , 1984, PODS.

[138]  Hans-Peter Kriegel,et al.  PLOP-hashing: A grid file without directory , 1988, Proceedings. Fourth International Conference on Data Engineering.

[139]  Alan P. Sexton.  Querying Indexed Files , 1997, CDB.

[140]  GütingRalf Hartmut,et al.  Rule-based optimization and query processing in an extensible geometric database system , 1992 .

[141]  Akhil Kumar.  G-Tree: A New Data Structure for Organizing Multidimensional Data , 1994, IEEE Trans. Knowl. Data Eng..

[142]  Peter van Oosterom,et al.  Reactive Data Structures for Geographic Information Systems , 1993 .

[143]  Georgios Evangelidis,et al.  The hBP-tree: A Modified hB-tree Supporting Concurrency, Recovery and Node Consolidation , 1995, VLDB.

[144]  Jeff A. Bilmes,et al.  Tree-Based Access Methods for Spatial Databases: Implementation and Performance Evaluation , 1991, IEEE Trans. Knowl. Data Eng..

[145]  Hanan Samet,et al.  A population analysis for hierarchical data structures , 1987, SIGMOD '87.

[146]  Masao Sakauchi,et al.  The BD-Tree - A New N-Dimensional Data Structure with Highly Efficient Dynamic Characteristics , 1983, IFIP Congress.

[147]  BentleyJon Louis.  Multidimensional binary search trees used for associative searching , 1975 .

[148]  Ibrahim Kamel,et al.  Bulk insertion in dynamic r-trees , 1996 .

[149]  Hans-Werner Six,et al.  How to Split Buckets in Spatial Data Structures , 1992 .

[150]  David B. Lomet,et al.  Bounded index exponential hashing , 1983, TODS.

[151]  Bernd-Uwe Pagel,et al.  Towards an analysis of range query performance in spatial data structures , 1993, PODS '93.

[152]  Jack A. Orenstein.  Strategies for Optimizing the Use of Redundancy in Spatial Databases , 1989, SSD.

[153]  Peter Schmidty,et al.  MMM : A WWW-Based Method ManagementSystem for Using Software Modules Remotely , 1996 .

[154]  Bernd-Uwe Pagel,et al.  The Transformation Technique for Spatial Objects Revisited , 1993, SSD.

[155]  Hanan Samet,et al.  A qualitative comparison study of data structures for large line segment databases , 1992, SIGMOD '92.

[156]  R. Bayer,et al.  Organization and maintenance of large ordered indices , 1970, SIGFIDET '70.

[157]  Agnès Voisard,et al.  Thematic Map Modeling , 1989, SSD.

[158]  Hans-Peter Kriegel,et al.  Techniques for Design and Implementation of Efficient Spatial Access Methods , 1988, VLDB.

[159]  Michael Freeston.  On the Complexity of BV-tree Updates , 1997, CDB.

[160]  Beng Chin Ooi,et al.  Spatial indexing in binary decomposition and spatial bounding , 1991, Inf. Syst..

[161]  Alfred V. Aho,et al.  Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems , 1982 .

[162]  Christos H. Papadimitriou,et al.  Towards a theory of indexability , 1997, PODS 1997.

[163]  T. M. Williams,et al.  Optimizing Methods in Statistics , 1981 .

[164]  Gary D. Knott.  Hashing Functions , 1975, Comput. J..

[165]  Gershon Kedem,et al.  The quad-cif tree a data structure for h , 1981, DAC 1982.

[166]  Christos Faloutsos,et al.  Fractals for secondary key retrieval , 1989, PODS.

[167]  Jack A. Orenstein.  Multidimensional Tries Used for Associative Searching , 1982, Inf. Process. Lett..

[168]  Ralf Hartmut Güting,et al.  Realms: A Foundation for Spatial Data Types in Database Systems , 1993, SSD.

[169]  Peter Widmayer,et al.  Enclosing Many Boxes by an Optimal Pair of Boxes , 1992, STACS.

[170]  Antonin Guttman,et al.  R-trees: a dynamic index structure for spatial searching , 1984, SIGMOD '84.

[171]  Hans-Peter Kriegel,et al.  Multidimensional quantile hashing is very efficient for nonuniform distributions , 1989, Inf. Sci..

[172]  Bernd-Uwe Pagel,et al.  Window query-optimal clustering of spatial objects , 1995, PODS.

[173]  Jack A. Orenstein.  A comparison of spatial query processing techniques for native and parameter spaces , 1990, SIGMOD '90.

[174]  Douglas Comer,et al.  Ubiquitous B-Tree , 1979, CSUR.

[175]  Masao Sakauchi,et al.  A new tree type data structure with homogeneous nodes suitable for a very large spatial database , 1990, [1990] Proceedings. Sixth International Conference on Data Engineering.

[176]  Henry Fuchs,et al.  On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[177]  Hans-Werner Six,et al.  The R-file: an efficient access structure for proximity queries , 1990, [1990] Proceedings. Sixth International Conference on Data Engineering.

[178]  Christos Faloutsos,et al.  Hilbert R-tree: An Improved R-tree using Fractals , 1994, VLDB.

[179]  Walter A. Burkhard.  Interpolation-based index maintenance , 1983, BIT Comput. Sci. Sect..

[180]  Michael Stonebraker,et al.  Segment indexes: dynamic indexing techniques for multi-dimensional interval data , 1991, SIGMOD '91.

[181]  Yannis Manolopoulos,et al.  Performance of Nearest Neighbor Queries in R-Trees , 1997, ICDT.

[182]  Christos Faloutsos,et al.  DOT: A Spatial Access Method Using Fractals , 1991, ICDE.

[183]  Ekow J. Otoo,et al.  Balanced multidimensional extendible hash tree , 1985, PODS.

[184]  Makoto Nagao,et al.  A file organization for geographic information systems based on spatial proximity , 1983, Comput. Vis. Graph. Image Process..

[185]  Doron Rotem.  Spatial join indices , 1991, [1991] Proceedings. Seventh International Conference on Data Engineering.

[186]  Hermann Tropf,et al.  Multimensional Range Search in Dynamically Balanced Trees , 1981, Angew. Inform..

[187]  Hanan Samet,et al.  Storing a collection of polygons using quadtrees , 1985, TOGS.

[188]  Christos Faloutsos,et al.  Multiattribute hashing using Gray codes , 1986, SIGMOD '86.

[189]  V. Gaede.  Constraint Databases and Their Applications, Second International Workshop on Constraint Database Systems, CDB '97, Delphi, Greece, January 11-12, 1997, CP '96 Workshop on Constraints and Databases, Cambridge, MA, USA, August 19, 1996, Selected Papers , 1997, CDB.

[190]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .