A General Framework for Modeling and Processing Optimization Queries.

An optimization query asks for one or more data objects that maximize or minimize some function over the data set. We propose a general class of queries, model-based optimization queries, in which a generic model is used to define a wide variety of queries involving an optimization objective function and/or a set of constraints on the attributes. This model can be used to define optimization of linear and nonlinear expressions over object attributes as well as many existing query types studied in database research literature. A significant and important subset of this general model relevant to real-world applications include queries where the optimization function and constraints are convex. We cast such queries as members of the convex optimization (CP) model and provide a unified query processing framework for CP queries that I/O optimally accesses data and space partitioning index structures without changing the underlying structures. We perform experiments to show the generality of the technique and where possible, compare to techniques developed for specialized optimization queries. We find that we achieve nearly identical performance to the limited optimization query types with optimal solutions, while providing generic modeling and processing for a much broader class of queries, and while effectively handling problem constraints.