1. A method of performing a high-level multi-dimensional external query on a multi-structural database, comprising: receiving a set of objects, a set of dimensions, and a relation that defines a position of each object within each dimension; receiving the external query that includes a subset of the objects, a subset of the dimensions, an integer, and a quality function for evaluating a quality of any candidate non-overlapping collection from all candidate non-overlapping collections having a size that is less than or equal to the integer; and returning a non-overlapping collection from the candidate non-overlapping collections, wherein the quality of the returned non-overlapping collection as defined by the quality function is at least as great as the quality of any other candidate non-overlapping collection.