# Implementing data cubes efficiently

01 Jun 1996-Vol. 25, Iss: 2, pp 205-216

TL;DR: In this article, a lattice framework is used to express dependencies among views and greedy algorithms are presented to determine a good set of views to materialize, with a small constant factor of optimal.

Abstract: Decision support applications involve complex queries on very large databases. Since response times should be small, query optimization is critical. Users typically view the data as multidimensional data cubes. Each cell of the data cube is a view consisting of an aggregation of interest, like total sales. The values of many of these cells are dependent on the values of other cells in the data cube. A common and powerful query optimization technique is to materialize some or all of these cells rather than compute them from raw data each time. Commercial systems differ mainly in their approach to materializing the data cube. In this paper, we investigate the issue of which cells (views) to materialize when it is too expensive to materialize all views. A lattice framework is used to express dependencies among views. We present greedy algorithms that work off this lattice and determine a good set of views to materialize. The greedy algorithm performs within a small constant factor of optimal under a variety of models. We then consider the most common case of the hypercube lattice and examine the choice of materialized views for hypercubes in detail, giving some good tradeoffs between the space used and the average time to answer a query.

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08 Sep 2000TL;DR: This book presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects, and provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data.

Abstract: The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

23,600 citations

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24 Aug 2003TL;DR: An analysis framework based on submodular functions shows that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models, and suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.

Abstract: Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

5,887 citations

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01 Mar 1997

TL;DR: An overview of data warehousing and OLAP technologies, with an emphasis on their new requirements, is provided, based on a tutorial presented at the VLDB Conference, 1996.

Abstract: Data warehousing and on-line analytical processing (OLAP) are essential elements of decision support, which has increasingly become a focus of the database industry. Many commercial products and services are now available, and all of the principal database management system vendors now have offerings in these areas. Decision support places some rather different requirements on database technology compared to traditional on-line transaction processing applications. This paper provides an overview of data warehousing and OLAP technologies, with an emphasis on their new requirements. We describe back end tools for extracting, cleaning and loading data into a data warehouse; multidimensional data models typical of OLAP; front end client tools for querying and data analysis; server extensions for efficient query processing; and tools for metadata management and for managing the warehouse. In addition to surveying the state of the art, this paper also identifies some promising research issues, some of which are related to problems that the database research community has worked on for years, but others are only just beginning to be addressed. This overview is based on a tutorial that the authors presented at the VLDB Conference, 1996.

2,835 citations

01 Jan 2006

TL;DR: There have been many data mining books published in recent years, including Predictive Data Mining by Weiss and Indurkhya [WI98], Data Mining Solutions: Methods and Tools for Solving Real-World Problems by Westphal and Blaxton [WB98], Mastering Data Mining: The Art and Science of Customer Relationship Management by Berry and Linofi [BL99].

Abstract: The book Knowledge Discovery in Databases, edited by Piatetsky-Shapiro and Frawley [PSF91], is an early collection of research papers on knowledge discovery from data. The book Advances in Knowledge Discovery and Data Mining, edited by Fayyad, Piatetsky-Shapiro, Smyth, and Uthurusamy [FPSSe96], is a collection of later research results on knowledge discovery and data mining. There have been many data mining books published in recent years, including Predictive Data Mining by Weiss and Indurkhya [WI98], Data Mining Solutions: Methods and Tools for Solving Real-World Problems by Westphal and Blaxton [WB98], Mastering Data Mining: The Art and Science of Customer Relationship Management by Berry and Linofi [BL99], Building Data Mining Applications for CRM by Berson, Smith, and Thearling [BST99], Data Mining: Practical Machine Learning Tools and Techniques by Witten and Frank [WF05], Principles of Data Mining (Adaptive Computation and Machine Learning) by Hand, Mannila, and Smyth [HMS01], The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman [HTF01], Data Mining: Introductory and Advanced Topics by Dunham, and Data Mining: Multimedia, Soft Computing, and Bioinformatics by Mitra and Acharya [MA03]. There are also books containing collections of papers on particular aspects of knowledge discovery, such as Machine Learning and Data Mining: Methods and Applications edited by Michalski, Brakto, and Kubat [MBK98], and Relational Data Mining edited by Dzeroski and Lavrac [De01], as well as many tutorial notes on data mining in major database, data mining and machine learning conferences.

2,591 citations

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TL;DR: In this paper, a survey of the available data mining techniques is provided and a comparative study of such techniques is presented, based on a database researcher's point-of-view.

Abstract: Mining information and knowledge from large databases has been recognized by many researchers as a key research topic in database systems and machine learning, and by many industrial companies as an important area with an opportunity of major revenues. Researchers in many different fields have shown great interest in data mining. Several emerging applications in information-providing services, such as data warehousing and online services over the Internet, also call for various data mining techniques to better understand user behavior, to improve the service provided and to increase business opportunities. In response to such a demand, this article provides a survey, from a database researcher's point of view, on the data mining techniques developed recently. A classification of the available data mining techniques is provided and a comparative study of such techniques is presented.

2,327 citations

##### References

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TL;DR: It is proved that (1 - o(1) ln n setcover is a threshold below which setcover cannot be approximated efficiently, unless NP has slightlysuperpolynomial time algorithms.

Abstract: Given a collection ℱ of subsets of S = {1,…,n}, set cover is the problem of selecting as few as possible subsets from ℱ such that their union covers S,, and max k-cover is the problem of selecting k subsets from ℱ such that their union has maximum cardinality. Both these problems are NP-hard. We prove that (1 - o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low-order terms) between the ratio of approximation achievable by the greedy alogorithm (which is (1 - o(1)) ln n), and provious results of Lund and Yanakakis, that showed hardness of approximation within a ratio of (log2n) / 2 ≃0.72 ln n. For max k-cover, we show an approximation threshold of (1 - 1/e)(up to low-order terms), under assumption that P ≠ NP.

2,941 citations

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26 Feb 1996TL;DR: The data cube operator as discussed by the authors generalizes the histogram, cross-tabulation, roll-up, drill-down, and sub-total constructs found in most report writers.

Abstract: Data analysis applications typically aggregate data across many dimensions looking for unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zero-dimensional or one-dimensional answers. Applications need the N-dimensional generalization of these operators. The paper defines that operator, called the data cube or simply cube. The cube operator generalizes the histogram, cross-tabulation, roll-up, drill-down, and sub-total constructs found in most report writers. The cube treats each of the N aggregation attributes as a dimension of N-space. The aggregate of a particular set of attribute values is a point in this space. The set of points forms an N-dimensionaI cube. Super-aggregates are computed by aggregating the N-cube to lower dimensional spaces. Aggregation points are represented by an "infinite value": ALL, so the point (ALL,ALL,...,ALL, sum(*)) represents the global sum of all items. Each ALL value actually represents the set of values contributing to that aggregation.

2,308 citations

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TL;DR: This survey describes a wide array of practical query evaluation techniques for both relational and postrelational database systems, including iterative execution of complex query evaluation plans, the duality of sort- and hash-based set-matching algorithms, types of parallel query execution and their implementation, and special operators for emerging database application domains.

Abstract: Database management systems will continue to manage large data volumes. Thus, efficient algorithms for accessing and manipulating large sets and sequences will be required to provide acceptable performance. The advent of object-oriented and extensible database systems will not solve this problem. On the contrary, modern data models exacerbate the problem: In order to manipulate large sets of complex objects as efficiently as today's database systems manipulate simple records, query-processing algorithms and software will become more complex, and a solid understanding of algorithm and architectural issues is essential for the designer of database management software. This survey provides a foundation for the design and implementation of query execution facilities in new database management systems. It describes a wide array of practical query evaluation techniques for both relational and postrelational database systems, including iterative execution of complex query evaluation plans, the duality of sort- and hash-based set-matching algorithms, types of parallel query execution and their implementation, and special operators for emerging database application domains.

1,427 citations

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07 Apr 1997TL;DR: The authors give algorithms that automate the selection of summary tables and indexes, and present a family of algorithms of increasing time complexities, and prove strong performance bounds for them.

Abstract: On-line analytical processing (OLAP) is a recent and important application of database systems. Typically, OLAP data is presented as a multidimensional "data cube." OLAP queries are complex and can take many hours or even days to run, if executed directly on the raw data. The most common method of reducing execution time is to precompute some of the queries into summary tables (subcubes of the data cube) and then to build indexes on these summary tables. In most commercial OLAP systems today, the summary tables that are to be precomputed are picked first, followed by the selection of the appropriate indexes on them. A trial-and-error approach is used to divide the space available between the summary tables and the indexes. This two-step process can perform very poorly. Since both summary tables and indexes consume the same resource-space-their selection should be done together for the most efficient use of space. The authors give algorithms that automate the selection of summary tables and indexes. In particular, they present a family of algorithms of increasing time complexities, and prove strong performance bounds for them. The algorithms with higher complexities have better performance bounds. However, the increase in the performance bound is diminishing, and they show that an algorithm of moderate complexity can perform fairly close to the optimal.

545 citations

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11 Sep 1995

TL;DR: Generalized projections are introduced, that capture aggregations, groupbys, duplicate-eliminating projections (distinct and duplicate-preserving projections in a common unified framework), and powerful query rewrite rules for aggregate queries are developed that unify and extend rewrite rules previously known in the literature.

Abstract: In this paper we introduce generalized projections (G P an extension of duplicateeliminating projections, that capture aggregations, groupbys, duplicate-eliminating projections (distinctand duplicate-preserving projections in a common unified framework. Using G P s we extend well known and simple algorithms for SQL queries that use distinct projections to derive algorithms for queries using aggregations like sum, max, min, count, and avg. We develop powerful query rewrite rules for aggregate queries that unify and extend rewrite rules previously known in the literature. We then illustrate the power of our approach by solving a very practical and important problem in data warehousing: how to answer an aggregate query on base tables using materialized aggregate views (summary

392 citations