Discovery of association rules is an important database mining problem. Current algorithms for nding association rules require several passes over the analyzed database, and obviously the role of I/O overhead is very signi cant for very large databases. We present new algorithms that reduce the database activity considerably. Theidea is to pick a random sample, to ndusingthis sample all association rules that probably hold in the whole database, and then to verify the results with the restofthe database. The algorithms thus produce exact association rules, not approximations based on a sample. The approach is, however, probabilistic, and inthose rare cases where our sampling method does not produce all association rules, the missing rules can be found inasecond pass. Our experiments show that the proposed algorithms can nd association rules very e ciently in only onedatabase pass. 1

Query optimization is an integral part of relational database management systems. One important task in query optimization is selectivity estimation, that is, given a query P , we need to estimate the fraction of records in the database that satisfy P . Many commercial database systems maintain histograms to approximate the frequency distribution of values in the attributes of relations. In this paper, we present a technique based upon a multiresolution wavelet decomposition for building histograms on the underlying data distributions, with applications to databases, statistics, and simulation. Histograms built on the cumulative data distributions give very good approximations with limited space usage. We give fast algorithms for constructing histograms and using them in an on-line fashion for selectivity estimation. Our histograms also provide quick approximate answers to OLAP queries when the exact answers are not required. Our method captures the joint distribution of multiple attri...

Many current database systems use histograms to approximate the frequency distribution of values in the attributes of relations and based on them estimate query result sizes and access plan costs. In choosing among the various histograms, one has to balance between two conflicting goals: optimality, so that generated estimates have the least error, and practicality, so that histograms can be constructed and maintained efficiently. In this paper, we present both theoretical and experimental results on several issues related to this trade-off. Our overall conclusion is that the most effective approach is to focus on the class of histograms that accurately maintain the frequencies of a few attribute values and assume the uniform distribution for the rest, and choose for each relation the histogram in that class that is optimal for a self-join query. 1 Introduction Query optimizers of relational database systems decide on the most efficient access plan for a given query based on a variety...

Imagine yourself standing in front of an exquisite buffet filled with numerous delicacies. Your goal is to try them all out, but you need to decide in what order. What exchange of tastes will maximize the overall pleasure of your palate? Although much less pleasurable and subjective, that is the type of problem that query optimizers are called to solve. Given a query, there are many plans that a database management system (DBMS) can follow to process it and produce its answer. All plans are equivalent in terms of their final output but vary in their cost, i.e., the amount of time that they need to run. What is the plan that needs the least amount of time? Such query optimization is absolutely necessary in a DBMS. The cost difference between two alternatives can be enormous. For example, consider the following database schema, which will be...

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Random sampling is a standard technique for constructing (approximate) histograms for query optimization. However, any real implementation in commercial products requires solving the hard problem of determining "How much sampling is enough?" We address this critical question in the context of equi-height histograms used in many commercial products, including Microsoft SQL Server. We introduce a conservative error metric capturing the intuition that for an approximate histogram to have low error, the error must be small in all regions of the histogram. We then present a result establishing an optimal bound on the amount of sampling required for pre-specified error bounds. We also describe an adaptive page sampling algorithm which achieves greater efficiency by using all values in a sampled page but adjusts the amount of sampling depending on clustering of values in pages. Next, we establish that the problem of estimating the number of distinct values is provably difficult, but propose ...

) Jeffrey Scott Vitter Center for Geometric Computing and Department of Computer Science Duke University Durham, NC 27708--0129 USA jsv@cs.duke.edu Min Wang y Center for Geometric Computing and Department of Computer Science Duke University Durham, NC 27708--0129 USA minw@cs.duke.edu Bala Iyer Database Technology Institute IBM Santa Teresa Laboratory P.O. Box 49023 San Jose, CA 95161 USA balaiyer@vnet.ibm.com Abstract There has recently been an explosion of interest in the analysis of data in data warehouses in the field of On-Line Analytical Processing (OLAP). Data warehouses can be extremely large, yet obtaining quick answers to queries is important. In many situations, obtaining the exact answer to an OLAP query is prohibitively expensive in terms of time and/or storage space. It can be advantageous to have fast, approximate answers to queries. In this paper, we present an I/O-efficient technique based upon a multiresolution wavelet decomposition that yields an approximate a...

In a recent paper, we proposed adding a STOP AFTER clause to SQL to permit the cardinality of a query result to be explicitly limited by query writers and query tools. We demonstrated the usefulness of having this clause, showed how to extend a traditional cost-based query optimizer to accommodate it, and demonstrated via DB2-based simulations that large performance gains are possible when STOP AFTER queries are explicitly supported by the database engine. In this paper, we present several new strategies for efficiently processing STOP AFTER queries. These strategies, based largely on the use of range partitioning techniques, offer significant additional savings for handling STOP AFTER queries that yield sizeable result sets. We describe classes of queries where such savings would indeed arise and present experimental measurements that show the benefits and tradeoffs associated with the new processing strategies. 1

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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 approxim...