Range Queries in the R-Tree

In order to handle spatial data efficiently, as required in computer aided design and geo-data applications, a database system needs an mdex mechanism that ti help it retrieve data items quickly accordmg to their spatial locations However, traditional mdexmg methods are not well suited to data oblects of non-zero size located m multidimensional spaces In this paper we describe a dynarmc mdex structure called an R-tree winch meets this need, and give algorithms for searching and updatmg it. We present the results of a series of tests which indicate that the structure performs well, and conclude that it is useful for current database systems m spatial applications

1997

M-tree is a dynamic access method suitable to index generic "metric spaces", where the function used to compute the distance between any two objects satisfies the positivity, symmetry, and triangle inequality postulates. The M-tree design fulfills typical requirements of multimedia applications, where objects are indexed using complex features, and similarity queries can require application of time-consuming distance functions. In this paper we describe the basic search and management algorithms of M-tree, introduce several heuristic split policies, and experimentally evaluate them, considering both I/O and CPU costs. Results also show that M-tree performs better than R * -tree on highdimensional vector spaces. * This work has been partially supported by ESPRIT LTR project no. 9141, HERMES (Foundations of High Performance Multimedia Information Management Systems). P. Zezula has also been supported by Grants GACR No. 102/96/0986 and KON-TAKT No. PM96 S028.

Information Systems, 2006

In multi-dimensional databases the essential tool for accessing data is the range query (or window query). In this paper we introduce a new algorithm of processing range query in universal B-tree (UB-tree), which is an index structure for searching in multi-dimensional databases. The new range query algorithm (called the DRU algorithm) works efficiently, even for processing high-dimensional databases. In particular, using the DRU algorithm many of the UBtree inner nodes need not to be accessed. We explain the DRU algorithm using a simple geometric model, providing a clear insight into the problem. More specifically, the model exploits an interesting relation between the Z-curve and generalized quad-trees. We also present experimental results for the DRU algorithm implementation. r

1998

We investigate the usability and performance of the UB-Tree (universal B-Tree) for multidimensional data, as they arise in all relational databases and in particular in data- warehousing and data-mining applications. The UB-Tree is balanced and has all the guaranteed performance characteristics of B-Trees, i.e., it requires linear space for storage and logarithmic time for the basic operations of insertion, retrieval

2009

Mobile query processing is, currently, a very active research field. Range and nearest neighbor queries are commonly used in spatiotemporal databases and location based services (LBS). In this paper, we focus on finding nearest neighbors of a query point within a certain distance range. We propose a new indexing structure CN-tree, Compact N-tree, based on a recent indexing technique called N-tree. CN-tree joins efficiency of N-tree's data partitioning scheme to pertinent objects' approximation with minimal bounding rectangles of R-trees which are reported to be the best performing for range search. We show how we use the approximation in constructing CN-tree and, then, how this index can support range queries efficiently by minimizing computation of distances and avoiding overlapping of minimal bounding rectangles. The experimental results through the comparison with the well know R*-tree, show that the proposed CN-tree widely outperforms R*-tree as an in-memory index and it presents competitive performances when used as an in-disk index.

Keywords: Indexing; R* tree indexing; P+ tree indexing.

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.

2003

Similarity searches in multidimensional Nonordered Discrete Data Spaces (NDDS) are becoming increasingly important for application areas such as genome sequence databases. Existing indexing methods developed for multidimensional (ordered) Continuous Data Spaces (CDS) such as R-tree cannot be directly applied to an NDDS. This is because some essential geometric concepts/properties such as the minimum bounding region and the area of a region in a CDS are no longer valid in an NDDS. On the other hand, indexing methods based on metric spaces such as M-tree are too general to effectively utilize the data distribution characteristics in an NDDS. Therefore, their retrieval performance is not optimized. To support efficient similarity searches in an NDDS, we propose a new dynamic indexing technique, called the ND-tree. The key idea is to extend the relevant geometric concepts as well as some indexing strategies used in CDSs to NDDSs. Efficient algorithms for ND-tree construction are presented. Our experimental results on synthetic and genomic sequence data demonstrate that the performance of the ND-tree is significantly better than that of the linear scan and M-tree in high dimensional NDDSs.

2001

Nowadays feature vector based similarity search is increasingly emerging in database systems. Consequently, many multidimensional data index techniques have been widely introduced to database researcher community. These index techniques are categorized into two main classes: SP (space partitioning)/KD-tree-based and DP (data partitioning)/R-tree-based. Recently, a hybrid index structure has been proposed. It combines both SP/KDtree-based and DP/R-tree-based techniques to form a new, more efficient index structure. However, weaknesses are still existing in techniques above. In this paper, we introduce a novel and flexible index structure for multidimensional data, the SH-tree (Super Hybrid tree). Theoretical analyses show that the SHtree is a good combination of both techniques with respect to both presentation and search algorithms. It overcomes the shortcomings and makes use of their positive aspects to facilitate efficient similarity searches.

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...