Repairing Data Violations with Order Dependencies

Lexicographical order dependencies (ODs) are proposed to describe the relationships between two lexicographical ordering specifications with respect to lists of attributes, and are proved to be useful in query optimizations concerning ordered attributes. To take full advantage of ODs, the data instance is supposed to satisfy OD specifications. In practice, data are often found to violate given ODs, as demonstrated in recent studies on discovery of ODs. This highlights the quest for data repairing techniques for ODs, to restore consistency of the data with respect to ODs. New challenges arise since ODs convey order semantics beyond functional dependencies, and are specified on lists of attributes. In this paper, we make a first effort to develop techniques for repairing data violations with ODs. (1) We formalize the data repairing problem for ODs, and prove that it is NP-hard in the size of the data. (2) Despite the intractability, we develop effective heuristic algorithms to address the problem. (3) We experimentally evaluate the effectiveness and efficiency of our algorithms, using both real-life and synthetic data.