Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zero-dimensional or one-dimensional aggregates. Applications need the N-dimensional generalization of these operators. This paper defines that operator, called the data cube or simply cube. The cube operator generalizes the histogram, crosstabulation, roll-up, drill-down, and sub-total constructs found in most report writers. The novelty is that cubes are relations. Consequently, the cube operator can be imbedded in more complex non-procedural data analysis programs. The cube operator 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-dimensional cube. Super-aggregates are computed by aggregating the N-cube to lower dimensional spaces. This paper (1) explains the cube and roll-up operators, (2) shows how they fit in SQL, (3) explains how users can define new aggregate functions for cubes, and (4) discusses efficient techniques to compute the cube. Many of these features are being added to the SQL Standard.

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 on-line services over the Internet, also call for various data mining techniques to better understand user behavior, to improve the service provided, and to increase the business opportunities. In response to such a demand, this article is to provide 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.

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 nodeselection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

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. 1.

Application of data mining techniques to the World Wide Web, referred to as Web mining, has been the focus of several recent research projects and papers. However, there is no established vocabulary, leading to confusion when comparing research e orts. The term Web mining has been used intwo distinct ways. The rst, called Web content mining in this paper, is the process of information discovery from sources across the World Wide Web. The second, called Web usage mining, is the process of mining for user browsing and access patterns. In this paper we de ne Web mining and present an overview of the various research issues, techniques, and development e orts. We brie y describe WEBMINER, a system for Web usage mining, and conclude this paper by listing research issues. 1

At the heart of all OLAP or multidimensional data analysis applications is the ability to simultaneously aggregate across many sets of dimensions. Computing multidimensional aggregates is a performance bottleneck for these applications. This paper presents fast algorithms for computing a collection of groupbys. We focus on a special case of the aggregation problem -- computation of the CUBE operator. The CUBE operator requires computing group-bys on all possible combinations of a list of attributes, and is equivalent to the union of a number of standard group-by operations. We show howthe structure of CUBE computation can be viewed in terms of a hierarchy of group-by operations. Our algorithms extend sort-based and hash-based grouping methods with several optimizations, like combining common operations across multiple group-bys, caching, and using pre-computed group-bys for computing other group-bys. Empirical evaluation shows that the resulting algorithms give much better performance compared to straightforward methods. This paper combines work done concurrently on computing the data cube by two different teams as reported in [SAG96] and [DANR96].

The problem of answering queries using views is to find efficient methods of answering a query using a set of previously materialized views over the database, rather than accessing the database relations. The problem has received significant attention because of its relevance to a wide variety of data management problems, such as data integration, query optimization, and the maintenance of physical data independence. To date, the performance of proposed algorithms has received very little attention, and in particular, their scale up in the presence of a large number of views is unknown. We first analyze two previous algorithms, the bucket algorithm and the inverse-rules algorithm, and show their deficiencies. We then describe the MiniCon algorithm, a novel algorithm for finding the maximally-contained rewriting of a conjunctive query using a set of conjunctive views. We present the first experimental study of algorithms for answering queries using views. The study shows that the MiniCon algorithm scales up well and significantly outperforms the previous algorithms. Finally, we describe an extension of the MiniCon algorithm to handle comparison predicates, and show its performance experimentally.

. A data warehouse stores materialized views of data from one or more sources, with the purpose of efficiently implementing decisionsupport or OLAP queries. One of the most important decisions in designing a data warehouse is the selection of materialized views to be maintained at the warehouse. The goal is to select an appropriate set of views that minimizes total query response time and the cost of maintaining the selected views, given a limited amount of resource, e.g., materialization time, storage space etc. In this article, we develop a theoretical framework for the general problem of selection of views in a data warehouse. We present competitive polynomial-time heuristics for selection of views to optimize total query response time, for some important special cases of the general data warehouse scenario, viz.: (i) an AND view graph, where each query/view has a unique evaluation, and (ii) an OR view graph, in which any view can be computed from any one of its related views, e.g.,...

Computing multidimensional aggregates in high dimensions is a performance bottleneck for many OLAP applications. Obtaining the exact answer to an aggregation query can be prohibitively expensive in terms of time and/or storage space in a data warehouse environment. It is advantageous to have fast, approximate answers to OLAP aggregation queries. In this paper, we present anovel method that provides approximate answers to high-dimensional OLAP aggregation queries in massive sparse data sets in a time-efficient and space-efficient manner. We construct a compact data cube, which is an approximate and space-efficient representation of the underlying multidimensional array, based upon a multiresolution wavelet decomposition. In the on-line phase, each aggregation query can generally be answered using the compact data cube in one I/O or a small number of I/Os, depending upon the desired accuracy. We present two I/O-efficient algorithms to construct the compact data cube for the important case of sparse high-dimensional arrays, which often arise in practice. The traditional histogram methods are infeasible for the massive high-dimensional data sets in OLAP applications. Previously developed wavelet techniques are efficient only for dense data. Our on-line query processing algorithm is very fast and capable of refining answers as the user demands more accuracy. Experiments on real data show that our method provides significantly more accurate results for typical OLAP aggregation queries than other efficient approximation techniques such as random sampling.

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. In this paper, we give algorithms that automate the selection of s...