A foreign/primary key relationship between relational tables is one of the most important constraints in a database. From a data analysis perspective, discovering foreign keys is a crucial step in understanding and working with the data. Nevertheless, more often than not, foreign key constraints are not specified in the data, for various reasons; e.g., some associations are not known to designers but are inherent in the data, while others become invalid due to data inconsistencies. This work proposes a robust algorithm for discovering single-column and multi-column foreign keys. Previous work concentrated mostly on discovering single-column foreign keys using a variety of rules, like inclusion dependencies, column names, and minimum/maximum values. We first propose a general rule, termed Randomness, that subsumes a variety of other rules. We then develop efficient approximation algorithms for evaluating randomness, using only two passes over the data. Finally, we validate our approach via extensive experiments using real and synthetic datasets.

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