Database columns are often correlated, so that cardinality estimates computed by assuming independence often lead to a poor choice of query plan by the optimizer. Multidimensional histograms can help solve this problem, but the traditional approach of building such histograms using a data scan often scales poorly and does not always yield the best histogram for a given workload. An attractive alternative is to gather feedback from the query execution engine about the observed cardinality of predicates and use this feedback as the basis for a histogram. In this paper we describe ISOMER, a new feedback-based algorithm for collecting optimizer statistics by constructing and maintaining multidimensional histograms. ISOMER uses the maximumentropy principle to approximate the true data distribution by a histogram distribution that is as "simple" as possible while being consistent with the observed predicate cardinalities. ISOMER adapts readily to changes in the underlying data, automatically detecting and eliminating inconsistent feedback information in an efficient manner. The algorithm controls the size of the histogram by retaining only the most "important" feedback. Our experiments indicate that, unlike previous methods for feedback-driven histogram maintenance, ISOMER imposes little overhead, is extremely scalable, and yields highly accurate cardinality estimates while using only a modest amount of storage.

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