A class of data structures for associative searching

Orenstein, Jack A.; Merrett, T. H.

doi:10.1145/588011.588037

Cited by 279 publications

(145 citation statements)

References 17 publications

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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%

“…Our pilot implementation has some similarity to the zkd-B-Tree approach described in [OM84]. We also use the Z-curve to to transform multidimensional point data into one-dimensional data.…”

Section: Multidimensional Access Methodsmentioning

confidence: 99%

“…Using the Lebesgue-curve (Z-curve) it is a variant of the zkd-B-Tree [OM84]. The UB-Tree utilizes a B * -Tree to store the Zaddresses of a Z-region partitioning of the multidimensional space.…”

Section: T 41 Concept Of the Ub-treementioning

confidence: 99%

“…The Z-address as primary key then leads to a multidimensional clustering [OM84]. However, this approach does not offer control over region boundaries during a page split; the region boundaries are defined by the tuples in this case.…”

Section: Basic Implementation Conceptsmentioning

confidence: 99%

“…However, using any variant of R-Trees [Gut84, BKS+90, BKK96] may result in a sub-optimal performance, since R-Trees may subdivide the universe into overlapping tiles, which may result in multiple accesses to one disk page. Therefore the most interesting candidates are Grid-Files [NHS84], hB-Trees [LS90], or space filling curves in combination with one-dimensional access methods [OM84,Jag90]. It is very well suitable for the UB-Tree, since the UB-Tree hierarchically organizes the data space.…”

Section: Addressing Sparsitymentioning

confidence: 99%

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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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Section: Multidimensional Access Methodsmentioning

confidence: 99%

“…Our pilot implementation has some similarity to the zkd-B-Tree approach described in [OM84]. We also use the Z-curve to to transform multidimensional point data into one-dimensional data.…”

Section: Multidimensional Access Methodsmentioning

confidence: 99%

Section: T 41 Concept Of the Ub-treementioning

confidence: 99%

Section: Basic Implementation Conceptsmentioning

confidence: 99%

Section: Addressing Sparsitymentioning

confidence: 99%

See 3 more Smart Citations

MISTRAL: Processing Relational Queries using a Multidimensional Access Technique

Markl

2000

Ausgezeichnete Informatikdissertationen 1999

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Data Distribution Management

Sarbazi-Azad

Zomaya

2013

Large Scale Network‐Centric Distributed Systems

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Efficient range query processing over DHTs based on the balanced Kautz tree

Zhang

Liu

et al. 2010

Concurrency and Computation

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SUMMARY Distributed Hash Tables (DHTs) are scalable, self-organizing, and adaptive to underlying topology changes, thus being a promising infrastructure for hosting large-scale distributed applications. The ever-wider use of DHT infrastructures has found more and more applications that require support for range queries. Recently, a number of DHT-based range query schemes have been proposed. However, most of them suffer from high query delay or imbalanced load distribution. To address these problems, in this paper we first present an efficient indexing structure called Balanced Kautz (BK) tree that uniformly maps the m-dimensional data space onto DHT nodes, and then propose a BK tree-based range query scheme called ERQ that processes range queries in a parallel fashion and guarantees to return the results in a bounded delay. In a DHT with N nodes, ERQ can answer any range of query in less than log N (2 log log N +1) hops in a load-balanced manner, irrespective of the queried range, the whole space size, or the number of queried attributes. The effectiveness of our proposals is demonstrated through experiments.

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A class of data structures for associative searching

Cited by 279 publications

References 17 publications

MISTRAL: Processing Relational Queries using a Multidimensional Access Technique

MISTRAL: Processing Relational Queries using a Multidimensional Access Technique

Data Distribution Management

Efficient range query processing over DHTs based on the balanced Kautz tree

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