In this demonstration paper, we describe iORDER, a tool that identifies implicit domain orders in data, such as Small Medium Large. iORDER extends the machinery of order dependency discovery to identify and rank interesting orders. Using real-world data, we showcase how implicit orders help users interpret the semantics of ordered data, how to interactively validate implicit orders to aid in the discovery process, and how to apply implicit orders to applications including data profiling, data mining and knowledge bases.

Most real-world data come with explicitly defined domain orders; e.g., lexicographic for strings, numeric for integers, and chronological for time. Our goal is to discover implicit domain orders that we do not already know; for instance, that the order of months in the Chinese Lunar calendar is Corner$<$Apricot$<$Peach. To do so, we enhance data profiling methods by discovering implicit domain orders in data through order dependencies. We enumerate tractable special cases and show that the general case is NP-complete but can be effectively handled by a SAT solver. We also devise an interestingness measure to rank the discovered implicit domain orders. Based on an extensive suite of experiments with real-world data, we establish the efficacy of our algorithms.

Order dependencies (ODs) capture relationships between ordered domains of attributes. Approximate ODs (AODs) capture such relationships even when there exist exceptions in the data. During automated discovery of ODs, validation is the process of verifying whether an OD holds. We present an algorithm for validating approximate ODs with significantly improved runtime performance over existing methods for AODs, and prove that it is correct and has optimal runtime. By replacing the validation step in a leading algorithm for approximate OD discovery with ours, we achieve orders-of-magnitude improvements in performance.