An estimation algorithm for a query is a probabilistic algorithm that computes an approximation for the size (number of tuples) of the query. One class of estimation algorithms uses a form of statistical sampling known as adaptive sampling. Several versions of adaptive sampling have been developed by other researchers. The original version has been surpassed in some ways by a newer version and a more specialized Monte-Carlo algorithm. An analysis of the cost of the original version is presented, and the different algorithms are compared. The analysis is used to derive an upper bound on the number of samples required by the original algorithm. Also, contrary to what seems to be a commonly held opinion, none of the algorithms is generally better than the other two. Which algorithm is superior depends on the query being estimated and the criteria that are being applied. Another question that is studied is which classes of logically definable queries have fast estimation algorithms. Evidence from descriptive complexity theory is provided that indicates not all such queries have fast estimation algorithms. However, it is shown that on classes of structures of bounded degree, all first-order queries have fast estimation algorithms
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