Accurate and efficient cardinality estimation is of critical importance to many database operations. In this book, we study three cardinality estimation problems in the contexts of query optimization and data cleaning, and propose a set of new techniques to address the challenges arising therein. We first consider the problem of estimating the number of distinct value combinations for a set of attributes. We propose an estimator that utilizes the knowledge of marginal distributions of individual attributes, and establish upper and lower bounds on the estimate. In the second part of the book, we propose HASE, a hybrid approach to selectivity estimation. We formulate cardinality estimation as a constrained optimization problem, making consistent use of two sources of information (synopsis-based and sampling-based) when they are available. We provide algorithms and reason about the quality of the estimate. Finally, we study the problem of cardinality estimation for approximate joins, which are fundamental operations in data cleaning tasks. We propose two sampling-based schemes for estimation, one based on sampling tuples, and the other on sampling tokens.

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