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-of-lnagnitude performance improvements over the prior state-of-the-art.
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机译：完整性约束（ICS）是用于查询优化和表达和实施应用语义有用。然而，配制约束需要手工领域的专业知识，容易出现人为错误，并且可以是过于费时，特别是在大的数据集。因此，对于自动发现已经提出了对于某些类的IC，诸如函数依赖（FDS），和最近，顺序依赖性（ODS）。正确的OD文件描述符归入，因为它们可以另外表示涉及为了业务规则;例如，同时要降低税收比另一个雇员雇员从不具有更高的薪水。我们提出的一种新的多项式映射启用的消耗臭氧层物质的规范形成新的OD发现算法，并为规范消耗臭氧层物质健全一整套公理（推理规则）。我们的算法具有指数的最坏情况的时间复杂度，O（2〜（| R |）），在属性数| R |和线性元组的数目的复杂性。我们证明，它会产生一个完整的和最小的一组消耗臭氧层物质。使用真正的和合成的数据集，我们实验表明订单的-lnagnitude性能改进与现有的国家的最先进的。
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