Many commercial database systems maintain histograms to summarize the contents of relations and permit efficient estimation of query result sizes and access plan costs. Although several types of histograms have been proposed in the past, there has never been a systematic study of all histogram aspects, the available choices for each aspect, and the impact of such choices on histogram effectiveness. In this paper, we provide a taxonomy of histograms that captures all previously proposed histogram types and indicates many new possibilities. We introduce novel choices for several of the taxonomy dimensions, and derive new histogram types by combining choices in effective ways. We also show how sampling techniques can be used to reduce the cost of histogram construction. Finally, we present results from an empirical study of the proposed histogram types used in selectivity estimation of range predicates and identify the histogram types that have the best overall performance. 1 Introduction...

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...

The result size of a query that involves multiple attributes from the same relation depends on these attributes’joinr data distribution, i.e., the frequencies of all combinations of attribute values. To simplify the estimation of that size, most commercial systems make the artribute value independenceassumption and maintain statistics (typically histograms) on individual attributes only. In reality, this assumption is almost always wrong and the resulting estimations tend to be highly inaccurate. In this paper, we propose two main alternatives to effectively approximate (multi-dimensional) joint data distributions. (a) Using a multi-dimensional histogram, (b) Using the Singular Value Decomposition (SVD) technique from linear algebra. An extensive set of experiments demonstrates the advantages and disadvantages of the two approaches and the benefits of both compared to the independence assumption. 1

XML is an emerging standard for data representation and exchange on the World-Wide Web. Due to the nature of information on the Web and the inherent flexibility of XML, we expect that much of the data encoded in XML will be semistructured:the data may be irregular or incomplete, and its structure may change rapidly or unpredictably. This paper describes the query processor of Lore,aDBMS for XML-based data supporting an expressive query language. We focus primarily on Lore's cost-based query optimizer. While all of the usual problems associated with cost-based query optimization apply to XML-based query languages, a number of additional problems arise, such as new kinds of indexing, more complicated notions of database statistics, and vastly different query execution strategies for different databases. We define appropriate logical and physical query plans, database statistics, and a cost model, and we describe plan enumeration including heuristics for reducing the large search space. Our optimizer is fully implemented in Lore and preliminary performance results are reported.

Rapid advances in networking and Internet technologies have fueled the emergence of the "software as a service" model for enterprise computing. Successful examples of commercially viable software services include rent-a-spreadsheet, electronic mail services, general storage services, disaster protection services. "Database as a Service" model provides users power to create, store, modify, and retrieve data from anywhere in the world, as long as they have access to the Internet. It introduces several challenges, an important issue being data privacy. It is in this context that we specifically address the issue of data privacy.

Recently we have proposed an adaptive, random sampling algorithm for general query size estimation. In earlier work we analyzed the asymptotic efficiency and accuracy of the algorithm; in this paper we investigate its practicality as applied to selects and joins. First, we extend our previous analysis to provide significantly improved bounds on the amount of sampling necessary for a given level of accuracy. Next, we provide "sanity bounds" to deal with queries for which the underlying data is extremely skewed or the query result is very small. Finally, we report on the performance of the estimation algorithm as implemented in a host language on a commercial relational system. The results are encouraging, even with this loose coupling between the estimation algorithm and the DBMS.

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...

We present new algorithms for computing approximate quantiles of large datasets in a single pass. The approximation guarantees are explicit, and apply without regard to the value distribution or the arrival distributions of the dataset. The main memory requirements are smaller than those reported earlier by an order of magnitude. We also discuss methods that couple the approximation algorithms with random sampling to further reduce memory requirements. With sampling, the approximation guarantees are explicit but probabilistic, i.e., they apply with respect to a (user controlled) confidence parameter. We present the algorithms, their theoretical analysis and simulation results. 1 Introduction This article studies the problem of computing order statistics of large sequences of online or disk-resident data using as little main memory as possible. We focus on computing quantiles, which are elements at specific positions in the sorted order of the input. The OE-quantile, for OE 2 [0; ...

There has been extensive work in query optimization since the early ‘70s. It is hard to capture the breadth and depth of this large body of work in a short article. Therefore, I have decided to focus primarily on the optimization of SQL queries in relational database systems and present my biased and incomplete view of this field. The goal of this article is not to be comprehensive, but rather to explain the foundations and present samplings of significant work in this area. I would like to apologize to the many contributors in this area whose work I have failed to explicitly acknowledge due to oversight or lack of space. I take the liberty of trading technical precision for ease of presentation. 2.