Multi-dimensional Range Queries Research Articles

Optimizing bitmap indices with efficient compression

Bitmap indices are efficient for answering queries on low-cardinality attributes. In this article, we present a new compression scheme called Word-Aligned Hybrid (WAH) code that makes compressed bitmap indices efficient even for high-cardinality attributes. We further prove that the new compressed bitmap index, like the best variants of the B-tree index, is optimal for one-dimensional range queries. More specifically, the time required to answer a one-dimensional range query is a linear function of the number of hits. This strongly supports the well-known observation that compressed bitmap indices are efficient for multidimensional range queries because results of one-dimensional range queries computed with bitmap indices can be easily combined to answer multidimensional range queries. Our timing measurements on range queries not only confirm the linear relationship between the query response time and the number of hits, but also demonstrate that WAH compressed indices answer queries faster than the commonly used indices including projection indices, B-tree indices, and other compressed bitmap indices.

Selectivity estimators for multidimensional range queries over real attributes

Estimating the selectivity of multidimensional range queries over real valued attributes has significant applications in data exploration and database query optimization. In this paper, we consider the following problem: given a table of d attributes whose domain is the real numbers and a query that specifies a range in each dimension, find a good approximation of the number of records in the table that satisfy the query. The simplest approach to tackle this problem is to assume that the attributes are independent. More accurate estimators try to capture the joint data distribution of the attributes. In databases, such estimators include the construction of multidimensional histograms, random sampling, or the wavelet transform. In statistics, kernel estimation techniques are being used. Many traditional approaches assume that attribute values come from discrete, finite domains, where different values have high frequencies. However, for many novel applications (as in temporal, spatial, and multimedia databases) attribute values come from the infinite domain of real numbers. Consequently, each value appears very infrequently, a characteristic that affects the behavior and effectiveness of the estimator. Moreover, real-life data exhibit attribute correlations that also affect the estimator. We present a new histogram technique that is designed to approximate the density of multidimensional datasets with real attributes. Our technique defines buckets of variable size and allows the buckets to overlap. The size of the cells is based on the local density of the data. The use of overlapping buckets allows a more compact approximation of the data distribution. We also show how to generalize kernel density estimators and how to apply them to the multidimensional query approximation problem. Finally, we compare the accuracy of the proposed techniques with existing techniques using real and synthetic datasets. The experimental results show that the proposed techniques behave more accurately in high dimensionalities than previous approaches.

On a model of indexability and its bounds for range queries

We develop a theoretical framework to characterize the hardness of indexing data sets on block-access memory devices like hard disks. We define an indexing workload by a data set and a set of potential queries. For a workload, we can construct an indexing scheme, which is a collection of fixed-sized subsets of the data. We identify two measures of efficiency for an indexing scheme on a workload: storage redundancy, r (how many times each item in the data set is stored), and access overhead, A (how many times more blocks than necessary does a query retrieve).For many interesting families of workloads, there exists a trade-off between storage redundancy and access overhead. Given a desired access overhead A , there is a minimum redundancy that any indexing scheme must exhibit. We prove a lower-bound theorem for deriving the minimum redundancy. By applying this theorem, we show interesting upper and lower bounds and trade-offs between A and r in the case of multidimensional range queries and set queries.

DHR-Trees: A Distributed Multidimensional Indexing Structure for P2P Systems

Supporting range query over Peer-to-Peer systems has attracted many research efforts in recent years. In this paper, we propose a new multidimensional indexing structure for P2P systems called Distributed Hilbert R-trees (DHR-trees). DHR-trees enables multidimensional range query to be executed similarly as in overlapping regions tree in P2P systems. Its distributed structure makes it fault-tolerant and scalable to dynamic network environment with a large number of peers as well. Our experiments shows that it performs well on multidimensional range query while the maintenance cost is reasonably low.

Practical Aspects of Large-Scale Distributed Computing

In the exciting and rapidly moving world of parallel and distributed computing, advances in these multi-faceted fields need to be evaluated early and disseminated quickly. The International Symposium on Parallel and Distributed Computing (ISPDC), as well as Scalable Computing—Practice and Experience (SCPE), attempts to provide interactive, professional, and friendly forums for these purposes. Following the ISPDC meetings in Lille in 2005, Cork in 2004, Slovenia in 2003, Iasi in 2002, the 5th ISPDC meeting was held in Timisoara, Romania, from July 6th to 9th 2006. Of the 84 submissions received, 45 were chosen for delivery and inclusion in the IEEE Computer Press post-proceedings. These papers were limited to eight pages, thus the authors of the best papers were invited to publish extended versions of their contributions in SCPE. Nine cutting edge papers were selected for publication in this issue. The first paper, by Emmanuel Jeanvoine, Louis Rilling, Christine Morin, and Daniel Leprince, presents Vigne, a Grid operating system that deals with the huge number of nodes and their dynamic behavior by using peer-to-peer overlays. In the second paper, Ivan Frain, Abdelaziz M'Zoughi, and Jean-Paul Bahsoun introduce a dynamic quorum protocol, called the elementary permutation protocol, that permits the dynamic reconfiguration of a tree-structured coterie in function of the load of the machines that possess data replicas. The third paper, by Ricolindo Carino and Ioana Banicescu, describes a dynamic load balancing tool intended to simplify the conversion of sequential programs containing computationally intensive one- or two-dimensional loops with independent iterates into parallel programs that execute with high efficiency on general-purpose clusters. In the fourth paper, Miguel Bernabeu, Mariam Taroncher, Victor Garcia, and Ana Vidal describe a parallel implementation of a Lanczos-based method to solve generalized eigenvalue problems related to the modal computation of arbitrarily shaped waveguides. Ouissem Ben Fredj and Eric Renault presents in the fifth paper of this issue the design of InfiniWrite, an implementation of the lightweight communication interface RWAPI over a Grid infrastructure called GRWA. The sixth paper, by Keith Rochford, Brian Coghlan and John Walsh, describes the design and implementation of an agent-based architecture capable of detecting and aggregating status information using low-level sensors, functionality tests and existing information systems. In the seventh paper, Xinfa Wei and Kaoru Sezaki propose a new multidimensional indexing structure for P2P systems called Distributed Hilbert R-trees that enables fault-tolerant, scalable, and multidimensional range query to be executed similarly as in overlapping regions tree in P2P systems. Maria Lopez, Elisa Heymann and Miquel Senar analyze, in the eight paper of this issue, several heuristics used as static and dynamic scheduling strategies in a Grid environment and classify them according different practical criteria. Finally, the ninth paper, by Rocco Aversa, Beniamino Di Martino, Salvatore Venticinque and Nicola Mazzoca, describes the functional model, the architecture design and the prototypal implementation of a platform called MAgDA, for services adaptation and delivery using agent technologies. Note that the above mentioned papers represents different topics covered by ISPDC and SCPE that are intensively studied in the last years and we hope that the reader of this issue will find the papers interesting for his or her future research activities. Dana Petcu

SEE: a Spatial Exploration Environment based on a direct-manipulation paradigm

The need to provide effective tools for analyzing and querying spatial data is becoming increasingly important with the explosion of data in applications such as geographic information systems, image databases, CAD, and remote sensing. The SEE (Spatial Exploration Environment) is the first effort at applying direct-manipulation visual information seeking (VIS) techniques to spatial data analysis by visually querying as well as browsing spatial data and reviewing the visual results for trend analysis. The SEE system incorporates a visual query language (SVIQUEL) that allows users to specify the relative spatial position (both topology and direction) between objects using direct manipulation. The quantitative SVIQVEL sliders (S-sliders) are complemented by the qualitative active-picture-for-querying (APIQ) interface that allows the user to specify qualitative relative position queries. APIQ provides qualitative visual representations of the quantitative query specified by the S-sliders. This increases the utility of the system for spatial browsing and spatial trend discovery with no particular query in mind. The SVIQUEL queries are processed using a k-Bucket index structure specifically tuned for incremental processing of the multidimensional range queries that represent the class of queries that can be expressed by SVIQUEL. We have also designed a tightly integrated map visualization that helps to preserve the spatial context and a bar visualization that provides a qualitative abstraction of aggregates.

Approximating multi-dimensional aggregate range queries over real attributes

Finding approximate answers to multi-dimensional range queries over real valued attributes has significant applications in data exploration and database query optimization. In this paper we consider the following problem: given a table of d attributes whose domain is the real numbers, and a query that specifies a range in each dimension, find a good approximation of the number of records in the table that satisfy the query. We present a new histogram technique that is designed to approximate the density of multi-dimensional datasets with real attributes. Our technique finds buckets of variable size, and allows the buckets to overlap. Overlapping buckets allow more efficient approximation of the density. The size of the cells is based on the local density of the data. This technique leads to a faster and more compact approximation of the data distribution. We also show how to generalize kernel density estimators, and how to apply them on the multi-dimensional query approximation problem. Finally, we compare the accuracy of the proposed techniques with existing techniques using real and synthetic datasets.

Scalability analysis of declustering methods for multidimensional range queries

Efficient storage and retrieval of multi-attribute data sets has become one of the essential requirements for many data-intensive applications. The Cartesian product file has been known as an effective multi-attribute file structure for partial-match and best-match queries. Several heuristic methods have been developed to decluster Cartesian product files across multiple disks to obtain high performance for disk accesses. Although the scalability of the declustering methods becomes increasingly important for systems equipped with a large number of disks, no analytic studies have been done so far. The authors derive formulas describing the scalability of two popular declustering methods-Disk Module and Fieldwise Xor-for range queries, which are the most common type of queries. These formulas disclose the limited scalability of the declustering methods, and this is corroborated by extensive simulation experiments. From the practical point of view, the formulas given in the paper provide a simple measure that can be used to predict the response time of a given range query and to guide the selection of a declustering method under various conditions.