Effective and Complete Discovery of Order Dependencies via Set-based Axiomatization

Integrity constraints (ICs) are useful for query optimization and for expressing and enforcing application semantics. However, formulating constraints manually requires domain expertise, is prone to human errors, and may be excessively time consuming, especially on large datasets. Hence, proposals for automatic discovery have been made for some classes of ICs, such as functional dependencies (FDs), and recently, order dependencies (ODs). ODs properly subsume FDs, as they can additionally express business rules involving order; e.g., an employee never has a higher salary while paying lower taxes than another employee. We present a new OD discovery algorithm enabled by a novel polynomial mapping to a canonical form of ODs, and a sound and complete set of axioms (inference rules) for canonical ODs. Our algorithm has exponential worst-case time complexity, O(2|R|), in the number of attributes |R| and linear complexity in the number of tuples. We prove that it produces a complete and minimal set of ODs. Using real and synthetic datasets, we experimentally show orders-ofmagnitude performance improvements over the prior stateof-the-art.