The UB-Tree: Performance of Multidimensional Range Queries

2006

Multi-dimensional data structures are applied in many real index applications, i.e. data mining, indexing multimedia data, indexing nonstructured text documents and so on. Many index structures and algorithms have been proposed. There are two major approaches to multi-dimensional indexing. These are, data structures to indexing metric and vector spaces. The R-tree, R*-tree, and UB-tree are representatives of the vector data structures. These data structures provide efficient processing for many types of queries, i.e. point queries, range queries and so on. As far as the vector data structures are concerned the range query retrieves all points in defined hyper box in an n-dimensional space. The narrow range query is a significant type of the range query. Its processing is inefficient in the vector data structures. Moreover, the efficiency decreases from increase dimension of an indexed space. We depict an application of the signature for more efficient processing of narrow range queries. The approach puts the signature into the R-tree but native functionalities are preserved, i.e. the range query algorithm for general range query. The novel data structure is called the Signature R-tree. This data structure is more resistant to the curse of dimensionality.

2001

Only few multidimensional access methods have made their way into commercial relational DBMS. Even if a RDBMS ships with a multidimensional index, the multidimensional index usually is an add-on like Oracle SDO, which is not integrated into the SQL interpreter, query processor and query optimizer of the DBMS kernel. Our demonstration shows TransBase HyperCube, a commercial RDBMS, whose kernel fully integrates the UB-Tree, a multidimensional extension of the B-Tree. This integration was performed in an ESPRIT project funded by the European Commission. We put the main emphasis of our demonstration on the application of UB-Tree indexes in realworld databases for OLAP. However, we also address general issues of UB-Trees like creation, spacerequirements, or comparison to other indexing methods.

Citeseer

Since the main memory is expensive and volatile persistence data cannot be kept in main memory. Most databases utilize the secondary/tertiary storage. The main overhead of using a secondary storage is access time. This is usually high in multi-dimensional databases like OLTP that are characterized by recurrent updates and queries. The use of secondary/tertiary storage inherently suggests indexing. Indexing helps to retrieve/store the required data/ data segments faster than iterating through the table. Indexing enhances speed of querying. In multi-dimensional databases (like OLAP databases) the essential tool for accessing data is the range query (or window query). In extant databases, B-Trees and its variants are the convention for indexing. But the major setback of B-trees is that they are single attribute index structures. Which implies that the record of such database are ordered by a particular attribute usually but not necessarily the primary key. This limits range query restriction on one particular attribute of the table. The use of multiple B-trees indexing for various attributes of a table is the convention for achieving range query for other attributes. The use of multi-indexing is additive and poses so many drawbacks (additional space required and speed is hampered). With the exponential burst of data, there is need for a better data structure with efficient query algorithm that has high storage capacity and also considerably fast (algorithm) for multidimensional range queries. This paper discusses a multidimensional indexing structure that is fast and also consumes virtually equivalent space as though is a single attribute structure. Experiment show that the structure has multiplicative complexities and is immune to the curse of dimensionality.

BIT, 1981

2009

Semantic query optimization consists in restricting the search space in order to reduce the set of objects of interest for a query. This paper presents an indexing method based on UB-trees and a static analysis of the constraints associated to the views of the database and to any constraint expressed on attributes. The result of the static analysis is a partitioning of the object space into disjoint blocks. Through Space Filling Curve (SFC) techniques, each fragment (block) of the partition is assigned a unique identifier, enabling the efficient indexing of fragments by UB-trees. The search space corresponding to a range query is restricted to a subset of the blocks of the partition. This approach has been developed in the context of a KB-DBMS but it can be applied to any relational system.

Proc. of the 8th Int'l Conf. on Database Systems …, 2003

Distributed and Parallel Databases, 2005

Multidimensional indexing is concerned with the indexing of multi-attributed records, where queries can be applied on some or all of the attributes. Indexing multi-attributed records is referred to by the term multidimensional indexing because each record is viewed as a point in a multidimensional space with a number of dimensions that is equal to the number of attributes. The values of the point coordinates along each dimension are equivalent to the values of the corresponding attributes. In this paper, the PN-tree, a new index structure for multidimensional spaces, is presented. This index structure is an efficient structure for indexing multidimensional points and is parallel by nature. Moreover, the proposed index structure does not lose its efficiency if it is serially processed or if it is processed using a small number of processors. The PN-tree can take advantage of as many processors as the dimensionality of the space. The PN-tree makes use of B + -trees that have been developed and tested over years in many DBMSs. The PN-tree is compared to the Hybrid tree that is known for its superiority among various index structures. Experimental results show that parallel processing of the PN-tree reduces significantly the number of disk accesses involved in the search operation. Even in its serial case, the PN-tree outperforms the Hybrid tree for large database sizes.

We propose the PATRICIA-hypercube-tree, or PH-tree, a multi-dimensional data storage and indexing structure. It is based on binary PATRICIA-tries combined with hypercubes for efficient data access. Space efficiency is achieved by combining prefix sharing with a space optimised implementation. This leads to storage space requirements that are comparable or below storage of the same data in non-index structures such as arrays of objects. The storage structure also serves as a multi-dimensional index on all dimensions of the stored data. This enables efficient access to stored data via point and range queries. We explain the concept of the PH-tree and demonstrate the performance of a sample implementation on various datasets and compare it to other spatial indices such as the kD-tree. The experiments show that for larger datasets beyond 10^7 entries, the PH-tree increasingly and consistently outperforms other structures in terms of space efficiency, query performance and update performance. For some highly skewed datasets, it even shows super-constant performance, becoming faster for larger datasets.

1999