Benchmarking the UB-tree

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.

2014

Range queries are a widely-used type of similarity queries that find all objects within a given distance from the query object. In this paper, we propose an approximate range query algorithm for the NDtree, a multi-dimensional index for vectors with nonordered discrete components. By sacrificing a little accuracy, approximate algorithms generally can greatly improve search performance. Our proposed approximate algorithm maintains a priority queue of tree nodes whose bounding rectangles (BR) intersect the query sphere. But it only accesses a user-specified portion of the queue. We propose a novel volumebased weighting scheme for the priority queue. The idea is that tree nodes whose BR has a larger intersection with the query sphere contain more result objects, thus should be accessed earlier. A closed-form formula is derived to calculate the volume of an intersection. Our experimental study using both synthetic and real data shows that the proposed algorithm can significantly improve...

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

Submitten at VLDB, 2004

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.

2017

Efficient evaluation of selection predicates (e.g., range predicates) defined on multiple columns of the same table is a difficult, but nevertheless important task. As we have seen an enormous increase of data within the last decade, efficient multi-dimensional selection predicate evaluation becomes more important. This is especially important for scientific data management tasks, where we often face data sets that need to be filtered based on several dimensions. So far, the state-of-the-art solution strategy is to apply highly optimized sequential scans. However, the intermediate results are often large, while the final query result often only contains a small fraction of the data set. This is due to the combined selectivity of all predicates. We propose Elf a new tree-based approach to efficiently support such queries. Our structure indexes densely populated sub-spaces allowing for efficient pruning. Keywords— data analytics, indexing, main-memory databases, storage structures.

Information Systems, 1982

A new method for multiple attribute indexing, the Multidimensional B-Tree (MBDT), is developed. This method is well suited for dynamic databases, since it handles several types of associative queries efficiently and requires low-cost maintenance. Algorithms and search strategies for exact match, partial match, and range queries are presented and statistical procedures are given to estimate the average and worst case retrieval times. The applicability of our organization to practical databases is discussed and analytical tradeoffs with regard to index organizations based on k-d trees are established.

OLYMPIADS IN INFORMATICS, 2015

We present new results on Binary Indexed Trees in order to efficiently solve Range Minimum Queries. We introduce a way of using the Binary Indexed Trees so that we can answer different types of queries, e.g. the range minimum query, in O (log N) time complexity per operation, outperforming in speed similar data structures like Segment/Range Trees or the Sparse Table Algorithm.

2000

Multidimensional access methods like the UB-Tree can be used to accelerate almost any query processing operation, if proper query processing algorithms are used: Relational queries or SQL queries consist of restrictions, projections, ordering, grouping and aggregation, and join operations. In the presence of multidimensional restrictions or sorting, multidimensional range query or Tetris algorithms efficiently process these operations. In addition, these algorithms also efficiently support queries that generate some hierarchical restrictions (for instance by following 1:n foreign key relationships). In this paper we investigate the impacts on query processing in RDBMS when using UB-Trees and multidimensional hierarchical clustering for physical data organization. We illustrate the benefits by performance measurements of queries for a star schema from a real world application of a SAP business information warehouse. The performance results reported in this paper were measured with our prototype implementation of UB-Trees on top of Oracle 8. We compare the performance of UB-Trees to native query processing techniques of Oracle, namely access via an index organized table, which essentially stores a relation in a clustered B*-Tree, and access via a full table scan of an entire relation. In addition we measure the performance of the intersection of multiple bitmap indexes to answer multidimensional range queries.

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.

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