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...

We propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, star coordinates from NASA's Infrared-Ultraviolet Explorer etc.) we provide evidence that real data indeed are skewed, and, moreover, we show that they behave as mathematical fractals, with a measurable, non-integer fractal dimension. Armed with this tool, we then show its practical use in predicting the performance of spatial access methods, and specifically of the R-trees. We provide the first analysis of R-trees for skewed distributions of points: We develop a formula that estimates the number of disk accesses for range queries, given only the fractal dimension of the point set, and its count. Experiments on real data sets show that the formula is very accurate: the relative error is usually below 5%, and it rarely exceeds 10%. We believe that the fractal dimension will help rep...

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...

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We examine the estimation of selectivities for range and spatial join queries in real spatial databases. As we have shown earlier [FK94a], real point sets: (a) violate consistently the "uniformity" and "independence" assumptions, (b) can often be described as "fractals", with non-integer (fractal) dimension. In this paper we show that, among the infinite family of fractal dimensions, the so called "Correlation Dimension" D 2 is the one that we need to predict the selectivity of spatial join. The main contribution is that, for all the real and synthetic point-sets we tried, the average number of neighbors for a given point of the point-set follows a power law, with D 2 as the exponent. This immediately solves the selectivity estimation for spatial joins, as well as for "biased" range queries (i.e., queries whose centers prefer areas of high point density). We present the formulas to estimate the selectivity for the biased queries, including an integration constant (K `shape 0 ) for ea...

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...

In this paper, we propose a novel approach for estimating the record selectivities of database queries. The real attribute value distribution is adaptively approximated by a curve-fitting function using a query feedback mechanism. This approach has the advantages of requiring no extra database access overhead for gathering statistics and of being able to continuously adapt the value distribution through queries and updates. Experimental results show that the estimation accuracy of this approach is comparable to traditional methods based on statistics gathering. 1 Introduction In most database systems, the task of query optimization is to choose an efficient execution plan. Best plan selection requires accurate estimates of the costs of alternative plans. One of the most important factors that affects plan cost is selectivity, which is the number of tuples satisfying a given predicate. Therefore, in most cases, the accuracy of selectivity estimates directly affects the choice of best p...

In query-intensive database application areas, like decision support and data mining, systems that use vertical fragmentation have a significant performance advantage. In order to support relational or object oriented applications on top of such a fragmented data model, a flexible yet powerful intermediate language is needed. This problem has been successfully tackled in Monet, a modern extensible database kernel developed by our group. We focus on the design choices made in the Monet Interpreter Language (MIL), its algebraic query language, and outline how its concept of tactical optimization enhances and simplifies the optimization of complex queries. Finally, we summarize the experience gained in Monet by creating a highly efficient implementation of MIL.

Object-Relational database management systems allow knowledgeable users to de ne new data types, as well as new methods (operators) for the types. This exibility produces an attendant complexity, which must be handled in new ways for an Object-Relational database management system to be e cient. In this paper we study techniques for optimizing queries that contain time-consuming methods. The focus of traditional query optimizers has been on the choice of join methods and orders; selections have been handled by \pushdown " rules. These rules apply selections in an arbitrary order before as many joins as possible, using the assumption that selection takes no time. However, users of Object-Relational systems can embed complex methods in selections. Thus selections may take signi cant amounts of time, and the query optimization model must be enhanced. In this paper, we carefully de ne a query cost framework that incorporates both selectivity and cost estimates for selections. We develop an algorithm called Predicate Migration, and prove that it produces optimal plans for queries with expensive methods. We then describe our implementation of Predicate Migration in the commercial Object-Relational database management system Illustra, and discuss practical issues that a ect our earlier assumptions. We compare Predicate Migration to a variety of simpler optimization techniques, and demonstrate that Predicate Migration is the best general solution to date. The alternative techniques we presentmaybe useful for constrained workloads.

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