On Two Kinds of Dataset Decomposition

Abstract

We consider a Cartesian decomposition of datasets, i.e. finding datasets such that their unordered Cartesian product yields the source set, and some natural generalization of this decomposition. In terms of relational databases, this means reversing the SQL CROSS JOIN and INNER JOIN operators (the last is equipped with a test verifying the equality of a tables attribute to another tables attribute). First we outline a polytime algorithm for computing the Cartesian decomposition. Then we describe a polytime algorithm for computing a generalized decomposition based on the Cartesian decomposition. Some applications and relating problems are discussed.