Synopses for Query Optimization: A Space-Complexity Perspective

Database systems use precomputed synopses of data to estimate the cost of alternative plans during query optimization. A number of alternative synopsis structures have been proposed, but histograms are by far the most commonly used. While histograms have proved to be very effective in (cost estimation for) single-table selections, queries with joins have long been seen as a challenge; under a model where histograms are maintained for individual tables, a celebrated result of Ioannidis and Christodoulakis [1991] observes that errors propagate exponentially with the number of joins in a query.

In this article, we make two main contributions. First, we study the space complexity of using synopses for query optimization from a novel information-theoretic perspective. In particular, we offer evidence in support of histograms for single-table selections, including an analysis over data distributions known to be common in practice, and illustrate their limitations for join queries. Second, for a broad class of common queries involving joins (specifically, all queries involving only key-foreign key joins) we show that the strategy of storing a small precomputed sample of the database yields probabilistic guarantees that are almost space-optimal, which is an important property if these samples are to be used as database statistics. This is the first such optimality result, to our knowledge, and suggests that precomputed samples might be an effective way to circumvent the error propagation problem for queries with key-foreign key joins. We support this result empirically through an experimental study that demonstrates the effectiveness of precomputed samples, and also shows the increasing difference in the effectiveness of samples versus multidimensional histograms as the number of joins in the query grows.