Revisiting the cube lifecycle in the presence of hierarchies

On-line analytical processing (OLAP) typically involves complex aggregate queries over large datasets. The data cube has been proposed as a structure that materializes the results of such queries in order to accelerate OLAP. A significant fraction of the related work has been on Relational-OLAP (ROLAP) techniques, which are based on relational technology. Existing ROLAP cubing solutions mainly focus on “flat” datasets, which do not include hierarchies in their dimensions. Nevertheless, as shown in this paper, the nature of hierarchies introduces several complications into the entire lifecycle of a data cube including the operations of construction, storage, indexing, query processing, and incremental maintenance. This fact renders existing techniques essentially inapplicable in a significant number of real-world applications and mandates revisiting the entire cube lifecycle under the new perspective. In order to overcome this problem, the CURE algorithm has been recently proposed as an efficient mechanism to construct complete cubes over large datasets with arbitrary hierarchies and store them in a highly compressed format, compatible with the relational model. In this paper, we study the remaining phases in the cube lifecycle and introduce query-processing and incremental-maintenance algorithms for CURE cubes. These are significantly different from earlier approaches, which have been proposed for flat cubes constructed by other techniques and are inadequate for CURE due to its high compression rate and the presence of hierarchies. Our methods address issues such as cube indexing, query optimization, and lazy update policies. Especially regarding updates, such lazy approaches are applied for the first time on cubes. We demonstrate the effectiveness of CURE in all phases of the cube lifecycle through experiments on both real-world and synthetic datasets. Among the experimental results, we distinguish those that have made CURE the first ROLAP technique to complete the construction and usage of the cube of the highest-density dataset in the APB-1 benchmark (12 GB). CURE was in fact quite efficient on this, showing great promise with respect to the potential of the technique overall.     

Online mining of fuzzy multidimensional weighted association rules

This paper addresses the integration of fuzziness with On-Line Analytical Processing (OLAP) based association rules mining. It contributes to the ongoing research on multidimensional online association rules mining by proposing a general architecture that utilizes a fuzzy data cube for knowledge discovery. A data cube is mainly constructed to provide users with the flexibility to view data from different perspectives as some dimensions of the cube contain multiple levels of abstraction. The first step of the process described in this paper involves introducing fuzzy data cube as a remedy to the problem of handling quantitative values of dimensional attributes in a cube. This facilitates the online mining of fuzzy association rules at different levels within the constructed fuzzy data cube. Then, we investigate combining the concepts of weight and multiple-level to mine fuzzy weighted multi-cross-level association rules from the constructed fuzzy data cube. For this purpose, three different methods are introduced for single dimension, multidimensional and hybrid (integrates the other two methods) fuzzy weighted association rules mining. Each of the three methods utilizes a fuzzy data cube constructed to suite the particular method. To the best of our knowledge, this is the first effort in this direction. We compared the proposed approach to an existing approach that does not utilize fuzziness. Experimental results obtained for each of the three methods on a synthetic dataset and on the adult data of the United States census in year 2000 demonstrate the effectiveness and applicability of the proposed fuzzy OLAP based mining approach. OLAP is one of the most popular tools for on-line, fast and effective multidimensional data analysis. In the OLAP framework, data is mainly stored in data hypercubes (simply called cubes).     

Object-based selective materialization for efficient implementationof spatial data cubes

With a huge amount of data stored in spatial databases and the introduction of spatial components to many relational or object-relational databases, it is important to study the methods for spatial data warehousing and OLAP of spatial data. In this paper, we study methods for spatial OLAP, by integrating nonspatial OLAP methods with spatial database implementation techniques. A spatial data warehouse model, which consists of both spatial and nonspatial dimensions and measures, is proposed. Methods for the computation of spatial data cubes and analytical processing on such spatial data cubes are studied, with several strategies being proposed, including approximation and selective materialization of the spatial objects resulting from spatial OLAP operations. The focus of our study is on a method for spatial cube construction, called object-based selective materialization, which is different from cuboid-based selective materialization (proposed in previous studies of nonspatial data cube construction). Rather than using a cuboid as an atomic structure during the selective materialization, we explore granularity on a much finer level: that of a single cell of a cuboid. Several algorithms are proposed for object-based selective materialization of spatial data cubes, and a performance study has demonstrated the effectiveness of these techniques     

Approximate range–sum query answering on data cubes with probabilistic guarantees

Approximate range aggregate queries are one of the most frequent and useful kinds of queries for Decision Support Systems (DSS), as they are widely used in many data analysis tasks. Traditionally, sampling-based techniques have been proposed to tackle this problem. However, their effectiveness degrade when the underlying data distribution is skewed. Another approach based on the outlier management can limit the effect of data skews but fails to address other requirements of approximate range aggregate queries, such as error guarantees and query processing efficiency. In this paper, we present a technique that provides approximate answers to range aggregate queries on OLAP data cubes efficiently, with theoretical guarantees on the errors. Our basic idea is to build different data structures to manage outliers and the rest of the data. Carefully chosen outliers are organized in a quad-tree based indexing data structure to provide efficient access for query processing. A query-workload adaptive, tree-like synopsis data structure, called T unable P artition-Tree (TP-Tree), is proposed to organize samples extracted from non-outlier data. Our experiments clearly demonstrate the merits of our technique, by comparing with previous well-known techniques.     

High Performance OLAP and Data Mining on Parallel Computers

On-Line Analytical Processing (OLAP) techniques are increasingly being used in decision support systems to provide analysis of data. Queries posed on such systems are quite complex and require different views of data. Analytical models need to capture the multidimensionality of the underlying data, a task for which multidimensional databases are well suited. Multidimensional OLAP systems store data in multidimensional arrays on which analytical operations are performed. Knowledge discovery and data mining requires complex operations on the underlying data which can be very expensive in terms of computation time. High performance parallel systems can reduce this analysis time. Precomputed aggregate calculations in a Data Cube can provide efficient query processing for OLAP applications. In this article, we present algorithms for construction of data cubes on distributed-memory parallel computers. Data is loaded from a relational database into a multidimensional array. We present two methods, sort-based and hash-based for loading the base cube and compare their performances. Data cubes are used to perform consolidation queries used in roll-up operations using dimension hierarchies. Finally, we show how data cubes are used for data mining using Attribute Focusing techniques. We present results for these on the IBM-SP2 parallel machine. Results show that our algorithms and techniques for OLAP and data mining on parallel systems are scalable to a large number of processors, providing a high performance platform for such applications.     

New Algorithm for Computing Cube on Very Large Compressed Data Sets

Data compression is an effective technique to improve the performance of data warehouses. Since cube operation represents the core of online analytical processing in data warehouses, it is a major challenge to develop efficient algorithms for computing cube on compressed data warehouses. To our knowledge, very few cube computation techniques have been proposed for compressed data warehouses to date in the literature. This paper presents a novel algorithm to compute cubes on compressed data warehouses. The algorithm operates directly on compressed data sets without the need of first decompressing them. The algorithm is applicable to a large class of mapping complete data compression methods. The complexity of the algorithm is analyzed in detail. The analytical and experimental results show that the algorithm is more efficient than all other existing cube algorithms. In addition, a heuristic algorithm to generate an optimal plan for computing cube is also proposed     

The percentage cube

OLAP cubes provide exploratory query capabilities combining joins and aggregations at multiple granularity levels. However, cubes cannot intuitively or directly show the relationship between measures aggregated at different grouping levels. One prominent example is the percentage, which is widely used in most analytical applications. Considering this limitation, we introduce percentage cube as a generalized data cube that takes percentages as its basic measure. More precisely, a percentage cube shows the fractional relationship in every cuboid between each aggregated measure on several dimensions and its rolled-up measure aggregated by fewer dimensions. We propose the syntax and introduce query optimizations to materialize the percentage cube. We justify that percentage cubes are significantly harder to evaluate than standard data cubes because in addition to the exponential number of cuboids, there is an additional exponential number of grouping column pairs (grouping columns at the individual level and the total level) on which percentages are computed. We propose alternative methods to prune the cube to identify interesting percentages including a row count threshold, a percentage threshold, and selecting the top k percentages. We study percentage aggregations within the classification of distributive, algebraic, and holistic functions. Finally, we also consider the problem of incremental computation of percentage cube. Experiments compare our query optimizations with existing SQL functions, evaluate the impact and speed of lattice pruning methods and study the effectiveness of the incremental computation.     

Enabling OLAP in mobile environments via intelligent data cube compression techniques

The main drawbacks of handheld devices (small storage space, small size of the display screen, discontinuance of the connection to the WLAN etc) are often incompatible with the need of querying and browsing information extracted from enormous amounts of data which are accessible through the network. In this application scenario, data compression and summarization have a leading role: data in a lossy compressed format can be transmitted more efficiently than the original ones, and can be effectively stored in handheld devices (setting the compression ratio accordingly). In this paper, we introduce a very effective compression technique for multidimensional data cubes, and the system Hand-OLAP, which exploits this technique to allow handheld devices to extract and browse compressed two-dimensional OLAP views coming from multidimensional data cubes stored on a remote OLAP server localized on the wired network. Hand-OLAP effectively and efficiently enables OLAP in mobile environments, and also enlarges the potentialities of Decision Support Systems by taking advantage from the “naturally” decentralized nature of such environments. The idea which the system is based on is: rather than querying the original multidimensional data cubes, it may be more convenient to generate a compressed OLAP view of them, store such view into the handheld device, and query it locally (off-line), thus obtaining approximate answers that are suitable for OLAP applications.     

基于Hadoop的封闭直方图立方

封闭数据立方是一种有效的无损压缩技术,它去掉了数据立方中的冗余信息,从而有效降低了数据立方的存储空间、加快了计算速度,而且几乎不影响查询性能.Hadoop的MapReduce并行计算模型为数据立方的计算提供了技术支持,Hadoop的分布式文件系统HDFS为数据立方的存储提供了保障.为了节省存储空间、加快查询速度,在传统数据立方的基础上提出封闭直方图立方,它在封闭数据立方的基础上通过编码技术进一步节省了存储空间,通过建立索引加快了查询速度.Hadoop并行计算平台不论从扩展性还是均衡性都为封闭直方图立方提供了保证.实验证明:封闭直方图立方对数据立方进行了有效压缩,具有较高的查询性能,根据Hadoop的特点通过增加节点个数明显加快了计算速度.     

Approximate Query Processing in Cube Streams

Data cubes have become important components in most data warehouse systems and decision support systems. In such systems, users usually pose very complex queries to the online analytical processing (OLAP) system, and systems usually have to deal with a huge amount of data because of the large dimensionality of the sets; thus, approximating query processing has emerged as a viable solution. Specifically, the applications of cube streams handle multidimensional data sets in a continuous manner in contrast to the traditional cube approximation. Such an application collects data events for cube streams online, generates snapshots with limited resources, and keeps the approximated information in a synopsis memory for further analysis. Compared to the OLAP applications, applications of cube streams are subject to many more resource constraints on both the processing time and the memory and cannot be dealt with by existing methods due to the limited resources. In this paper, we propose the DAWA algorithm, which is a hybrid algorithm of discrete cosine transform (DCT) for data and the discrete wavelet transform (DWT), to approximate cube streams. Our algorithm combines the advantages of the high compression rate of DWT and the low memory cost of DCT. Consequently, DAWA requires much smaller working buffer and outperforms both DWT-based and DCT-based methods in execution efficiency. Also, it is shown that DAWA provides a good solution for an approximate query processing of cube streams with a small working buffer and a short execution time. The optimality of the DAWA algorithm is theoretically proved and empirically demonstrated by our experiments.     

Efficient aggregation algorithms for compressed data warehouses

Aggregation and cube are important operations for online analytical processing (OLAP). Many efficient algorithms to compute aggregation and cube for relational OLAP have been developed. Some work has been done on efficiently computing cube for multidimensional data warehouses that store data sets in multidimensional arrays rather than in tables. However, to our knowledge, there is nothing to date in the literature describing aggregation algorithms on compressed data warehouses for multidimensional OLAP. This paper presents a set of aggregation algorithms on compressed data warehouses for multidimensional OLAP. These algorithms operate directly on compressed data sets, which are compressed by the mapping-complete compression methods, without the need to first decompress them. The algorithms have different performance behaviors as a function of the data set parameters, sizes of outputs and main memory availability. The algorithms are described and the I/O and CPU cost functions are presented in this paper. A decision procedure to select the most efficient algorithm for a given aggregation request is also proposed. The analysis and experimental results show that the algorithms have better performance on sparse data than the previous aggregation algorithms     

A Genetic Selection Algorithm for OLAP Data Cubes

Multidimensional data analysis, as supported by OLAP (online analytical processing) systems, requires the computation of many aggregate functions over a large volume of historically collected data. To decrease the query time and to provide various viewpoints for the analysts, these data are usually organized as a multidimensional data model, called data cubes. Each cell in a data cube corresponds to a unique set of values for the different dimensions and contains the metric of interest. The data cube selection problem is, given the set of user queries and a storage space constraint, to select a set of materialized cubes from the data cubes to minimize the query cost and/or the maintenance cost. This problem is known to be an NP-hard problem. In this study, we examined the application of genetic algorithms to the cube selection problem. We proposed a greedy-repaired genetic algorithm, called the genetic greedy method. According to our experiments, the solution obtained by our genetic greedy method is superior to that found using the traditional greedy method. That is, within the same storage constraint, the solution can greatly reduce the amount of query cost as well as the cube maintenance cost.     

数据方体系统设计中的优化问题

支持实时查询的联机分析处理系统的设计是当前一个很重要的研究问题。其中常用的方法是使用数据方体来实现。对于出现频率较高的查询,可以给出对应的数据方体集,使得每个查询都可以直接得到回答。但是在设计基于方体的系统时,需要考虑以下两个问题:(1)数据方体的维护成本,(2)回答频繁查询的响应时间。在用户给出了维护成本上限和响应时间上限后,需要对数据方体集进行优化,使得系统能够满足用户的要求,并回答尽可能多的查询。文章给出了数据方体系统设计优化问题的定义,这是一个NP完全问题,并提出了贪心删除和贪心合并的近似算法。实验表明了算法的有效性。     

Parallel ROLAP Data Cube Construction on Shared-Nothing Multiprocessors

The pre-computation of data cubes is critical to improving the response time of On-Line Analytical Processing (OLAP) systems and can be instrumental in accelerating data mining tasks in large data warehouses. In order to meet the need for improved performance created by growing data sizes, parallel solutions for generating the data cube are becoming increasingly important. This paper presents a parallel method for generating data cubes on a shared-nothing multiprocessor. Since no (expensive) shared disk is required, our method can be used on low cost Beowulf style clusters consisting of standard PCs with local disks connected via a data switch. Our approach uses a ROLAP representation of the data cube where views are stored as relational tables. This allows for tight integration with current relational database technology.We have implemented our parallel shared-nothing data cube generation method and evaluated it on a PC cluster, exploring relative speedup, local vs. global schedule trees, data skew, cardinality of dimensions, data dimensionality, and balance tradeoffs. For an input data set of 2,000,000 rows (72 Megabytes), our parallel data cube generation method achieves close to optimal speedup; generating a full data cube of 227 million rows (5.6 Gigabytes) on a 16 processors cluster in under 6 minutes. For an input data set of 10,000,000 rows (360 Megabytes), our parallel method, running on a 16 processor PC cluster, created a data cube consisting of 846 million rows (21.7 Gigabytes) in under 47 minutes.     

Compressed Data Cube for Approximate OLAP Query Processing

Approximate query processing has emerged as an approach to dealing with the huge data volume and complex queries in the environment of data warehouse.In this paper,we present a novel method that provides approximate answers to OLAP queries.Our method is based on building a compressed (approximate) data cube by a clustering technique and using this compressed data cube to provide answers to queries directly,so it improves the performance of the queries.We also provide the algorithm of the OLAP queries and the confidence intervals of query results.An extensive experimental study with the OLAP council benchmark shows the effectiveness and scalability of our cluster-based approach compared to sampling.     

Compression and aggregation of Bayesian estimates for data intensive computing

Bayesian estimation is a major and robust estimator for many advanced statistical models. Being able to incorporate prior knowledge in statistical inference, Bayesian methods have been successfully applied in many different fields such as business, computer science, economics, epidemiology, genetics, imaging, and political science. However, due to its high computational complexity, Bayesian estimation has been deemed difficult, if not impractical, for large-scale databases, stream data, data warehouses, and data in the cloud. In this paper, we propose a novel compression and aggregation schemes (C&A) that enables distributed, parallel, or incremental computation of Bayesian estimates. Assuming partitioning of a large dataset, the C&A scheme compresses each partition into a synopsis and aggregates the synopsis into an overall Bayesian estimate without accessing the raw data. Such a C&A scheme can find applications in OLAP for data cubes, stream data mining, and cloud computing. It saves tremendous computing time since it processes each partition only once, enabling fast incremental update, and allows parallel processing. We prove that the compression is asymptotically lossless in the sense that the aggregated estimator deviates from the true model by an error that is bounded and approaches to zero when the data size increases. The results show that the proposed C&A scheme can make feasible OLAP of Bayesian estimates in a data cube. Further, it supports real-time Bayesian analysis of stream data, which can only be scanned once and cannot be permanently retained. Experimental results validate our theoretical analysis and demonstrate that our method can dramatically save time and space costs with almost no degradation of the modeling accuracy.     

The cgmCUBE project: Optimizing parallel data cube generation for ROLAP

On-line Analytical Processing (OLAP) has become one of the most powerful and prominent technologies for knowledge discovery in VLDB (Very Large Database) environments. Central to the OLAP paradigm is the data cube, a multi-dimensional hierarchy of aggregate values that provides a rich analytical model for decision support. Various sequential algorithms for the efficient generation of the data cube have appeared in the literature. However, given the size of contemporary data warehousing repositories, multi-processor solutions are crucial for the massive computational demands of current and future OLAP systems. In this paper we discuss the cgmCUBE Project, a multi-year effort to design and implement a multi-processor platform for data cube generation that targets the relational database model (ROLAP). More specifically, we discuss new algorithmic and system optimizations relating to (1) a thorough optimization of the underlying sequential cube construction method and (2) a detailed and carefully engineered cost model for improved parallel load balancing and faster sequential cube construction. These optimizations were key in allowing us to build a prototype that is able to produce data cube output at a rate of over one TeraByte per hour. Research supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).     

Compression and Aggregation for Logistic Regression Analysis in Data Cubes

Logistic regression is an important technique for analyzing and predicting data with categorical attributes. In this paper, We consider supporting online analytical processing (OLAP) of logistic regression analysis for multi-dimensional data in a data cube where it is expensive in time and space to build logistic regression models for each cell from the raw data. We propose a novel scheme to compress the data in such a way that we can reconstruct logistic regression models to answer any OLAP query without accessing the raw data. Based on a first-order approximation to the maximum likelihood estimating equations, we develop a compression scheme that compresses each base cell into a small compressed data block with essential information to support the aggregation of logistic regression models. Aggregation formulae for deriving high-level logistic regression models from lower level component cells are given. We prove that the compression is nearly lossless in the sense that the aggregated estimator deviates from the true model by an error that is bounded and approaches to zero when the data size increases. The results show that the proposed compression and aggregation scheme can make feasible OLAP of logistic regression in a data cube.     

Graph OLAP: a multi-dimensional framework for graph data analysis

Databases and data warehouse systems have been evolving from handling normalized spreadsheets stored in relational databases, to managing and analyzing diverse application-oriented data with complex interconnecting structures. Responding to this emerging trend, graphs have been growing rapidly and showing their critical importance in many applications, such as the analysis of XML, social networks, Web, biological data, multimedia data and spatiotemporal data. Can we extend useful functions of databases and data warehouse systems to handle graph structured data? In particular, OLAP (On-Line Analytical Processing) has been a popular tool for fast and user-friendly multi-dimensional analysis of data warehouses. Can we OLAP graphs? Unfortunately, to our best knowledge, there are no OLAP tools available that can interactively view and analyze graph data from different perspectives and with multiple granularities. In this paper, we argue that it is critically important to OLAP graph structured data and propose a novel Graph OLAP framework. According to this framework, given a graph dataset with its nodes and edges associated with respective attributes, a multi-dimensional model can be built to enable efficient on-line analytical processing so that any portions of the graphs can be generalized/specialized dynamically, offering multiple, versatile views of the data. The contributions of this work are three-fold. First, starting from basic definitions, i.e., what are dimensions and measures in the Graph OLAP scenario, we develop a conceptual framework for data cubes on graphs. We also look into different semantics of OLAP operations, and classify the framework into two major subcases: informational OLAP and topological OLAP. Second, we show how a graph cube can be materialized by calculating a special kind of measure called aggregated graph and how to implement it efficiently. This includes both full materialization and partial materialization where constraints are enforced to obtain an iceberg cube. As we can see, due to the increased structural complexity of data, aggregated graphs that depend on the underlying “network” properties of the graph dataset are much harder to compute than their traditional OLAP counterparts. Third, to provide more flexible, interesting and informative OLAP of graphs, we further propose a discovery-driven multi-dimensional analysis model to ensure that OLAP is performed in an intelligent manner, guided by expert rules and knowledge discovery processes. We outline such a framework and discuss some challenging research issues for discovery-driven Graph OLAP.