Effective and complete discovery of bidirectional order dependencies via set-based axioms

Integrity constraints (ICs) are useful for expressing and enforcing application semantics. Formulating ICs manually, however, requires domain expertise, is prone to human error, and can be exceedingly time-consuming. Thus, methods for automatic discovery have been developed for some classes of ICs, such as functional dependencies (FDs), and recently, order dependencies (ODs). ODs properly subsume FDs and can express business rules involving order; e.g., an employee who pays higher taxes has a higher salary than another employee. Bidirectional ODs further allow different ordering directions, ascending and descending, as in SQL’s order-by; e.g., a student with an alphabetically lower letter grade has a higher percentage grade than another student. We address the limitations of prior work on automatic OD discovery, which has factorial complexity, is incomplete, and is not concise. We present an efficient bidirectional OD discovery algorithm enabled by a novel polynomial mapping to a canonical form, and a sound and complete set of axioms for canonical bidirectional ODs to prune the search space. Our algorithm has exponential worst-case time complexity in the number of attributes and linear complexity in the number of tuples. We prove that it produces a complete and minimal set of bidirectional ODs, and we experimentally show orders of magnitude performance improvements over the prior state-of-the-art methodologies.