The extendible cell method for closest point problems

Tamminen, Markku

doi:10.1007/bf01934393

Cited by 41 publications

(20 citation statements)

References 13 publications

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“…The grid file [Nievergelt et al 1984], for example, uses a directory and a gridlike partition of the universe to answer an exact match query with exactly two disk accesses. Furthermore, there are multidimensional hashing schemes [Tamminen 1982;Kriegel andSeeger 1986, 1988], multilevel grid files [Whang and Krishnamurthy 1985;Hutflesz et al 1988b], and hash trees [Ouksel 1985;Otoo 1985], which organize the directory as a tree structure. Tree-based access methods are usually a generalization of the B-tree to higher dimensions, such as the k-d-B-tree [Robinson 1981] or the hB-tree [Lomet and Salzberg 1989].…”

Section: Multidimensional Access Methodsmentioning

confidence: 99%

“…He also proves that the average space occupancy of the data buckets is about 69% (ln 2). [Tamminen 1982]. Closely related to the grid file is the EXCELL method (Extendible CELL) proposed by Tamminen [1982].…”

Section: Multidimensional Access Methodsmentioning

confidence: 99%

“…[Tamminen 1982]. Closely related to the grid file is the EXCELL method (Extendible CELL) proposed by Tamminen [1982]. In contrast to the grid file, where the partitioning hyperplanes may be spaced arbitrarily, the EXCELL method decomposes the universe regularly: all grid cells are of equal size.…”

Section: Multidimensional Access Methodsmentioning

confidence: 99%

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Multidimensional access methods

1998

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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.

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Section: Multidimensional Access Methodsmentioning

confidence: 99%

Section: Multidimensional Access Methodsmentioning

confidence: 99%

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Multidimensional access methods

1998

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“…[GG97] distinguishes three categories of multidimensional point access methods: Techniques based on hashing (grid files [NHS84], EXCELL [Tam82], multi-level grid files [Hin85], twin grid files [HSW88b] and multidimensional hashing [Fal85,Fal88]), hierarchical access methods (K-D-B-Tree [Rob81], LSD-Tree [HSW89], Buddy Tree [SK90], BANG File [Fre87], hB-Tree [LS90], R-Trees [Gut84, SRF87, BKS+90, BKK96]) and space filling curves in combination with one-dimensional access methods [TH81,OM84,Jag90,AS83,FR89]. Yet another access technique is to use a combination of several one-dimensional access methods like inverted files [Lum70,MHW+90] or bitmap index intersection [OQ97].…”

Section: Multidimensional Access Methodsmentioning

confidence: 99%

MISTRAL: Processing Relational Queries using a Multidimensional Access Technique

Markl

2000

Ausgezeichnete Informatikdissertationen 1999

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PrefaceClassical one dimensional B-trees have been the standard access method of all commercial database systems for many years. This dissertation is a very promising effort to introduce universal B-trees (UB-trees), the multidimensional variant of Btrees, as a basic access method into the core of fundamental DB-technology. The universal relevance of UB-trees is a consequence of the fact, that every relation can be considered as a set of points in multidimensional space. UB-trees organize this space for efficient processing of the data, resulting for many types of queries in orders of magnitude improvement over classical methods.The thesis lays the theoretical foundations of UB-tress, predicts their performance by analytical models and validates these models by experiments using large real world databases and real life applications and queries from the field of datawarehousing. The need to sort data and intermediate results frequently is an annoying drawback of today' s query processing methods. In combination with the Tetris algorithm UBtrees allow to avoid sorting in most cases, leading to dramatic improvements of response time, storage requirement and overall query processing time.Adding a new access method requires to consider all aspects of database systems:-architecture of subsystems -query optimization -query processing -multiuser operation and synchronization -bulk loading -storage requirement -parallelism, etc.Since UB-trees rely on classical B-trees for their implementation, all of these issues can be solved in a satisfactory way and can be dealt with elegantly.The performance experiments reported in this thesis were carried out with an implementation of UB-trees as a middleware layer on top of SQL. Additional performance improvements can be gained by integrating the UB-tree technology in the kernel of database systems.This thesis is a cornerstone of the MISTRAL project. MISTRAL has the goal to introduce UB-trees as a new access method into database systems with the fascinating vision, to extend fundamental database technology in an essential way. MISTRAL is financially supported by SAP, Teijin, NEC, Hitachi, the European Commission, Project MDA, TAS, Gfk and Microsoft. Abstract:A multidimensional access method offering significant performance increases by intelligently partitioning the query space is applied to relational database management systems (RDBMS). We introduce a formal model for multidimensional partitioned relations and discuss several typical query patterns. The model identifies the significance of multidimensional range queries and sort operations. The discussion of current access methods gives rise to the need for a multidimensional partitioning of relations. A detailed analysis of space partitioning focussing especially on Z-ordering illustrates the principle benefits of multidimensional indexes. After describing the UB-Tree and its standard algorithms for insertion, deletion, point queries, and range queries, we introduce the spiral algorithm for nearest neighbor queries with UB-Tree...

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“…Grid files [114,88,128,133,135,143,134] are extensions of the fixed-grid method [102]. The fixed-grid method partitions the search space into hypercubes of known, fixed size, and group all the records contained in the same hypercube into a bucket.…”

Section: A2 Multidimensional Hashing and Grid Filesmentioning

confidence: 99%

Content-based Retrieval

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The extendible cell method for closest point problems

Cited by 41 publications

References 13 publications

Multidimensional access methods

Multidimensional access methods

MISTRAL: Processing Relational Queries using a Multidimensional Access Technique

Content-based Retrieval

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