We propose a class of integrity constraints for relational databases, referred to as conditional functional dependencies (CFDs), and study their applications in data cleaning. In contrast to traditional functional dependencies (FDs) that were developed mainly for schema design, CFDs aim at capturing the consistency of data by enforcing bindings of semantically related values. For static analysis of CFDs we investigate the consistency problem , which is to determine whether or not there exists a nonempty database satisfying a given set of CFDs, and the implication problem , which is to decide whether or not a set of CFDs entails another CFD. We show that while any set of transitional FDs is trivially consistent, the consistency problem is NP-complete for CFDs, but it is in PTIME when either the database schema is predefined or no attributes involved in the CFDs have a finite domain. For the implication analysis of CFDs, we provide an inference system analogous to Armstrong's axioms for FDs, and show that the implication problem is coNP-complete for CFDs in contrast to the linear-time complexity for their traditional counterpart. We also present an algorithm for computing a minimal cover of a set of CFDs. Since CFDs allow data bindings, in some cases CFDs may be physically large, complicating the detection of constraint violations. We develop techniques for detecting CFD violations in SQL as well as novel techniques for checking multiple constraints by a single query. We also provide incremental methods for checking CFDs in response to changes to the database. We experimentally verify the effectiveness of our CFD-based methods for inconsistency detection. This work not only yields a constraint theory for CFDs but is also a step toward a practical constraint-based method for improving data quality.

We propose a class of constraints, referred to as conditional functional dependencies (CFDs), and study their applications in data cleaning. In contrast to traditional functional dependencies (FDs)

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We study the satisfiability problem associated with XPath in the presence of DTDs. This is the problem of determining, given a query p in an XPath fragment and a DTD D, whether or not there exists an XML document T such that T conforms to D and the answer of p on T is nonempty. We consider a variety of XPath fragments widely used in practice, and investigate the impact of different XPath operators on satisfiability analysis. We first study the problem for negation-free XPath fragments with and without upward axes, recursion and data-value joins, identifying which factors lead to tractability and which to NP-completeness. We then turn to fragments with negation but without data values, establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion. We show that with negation the complexity ranges from PSPACE to EXPTIME. Moreover, when both data values and negation are in place, we find that the complexity ranges from NEXPTIME to undecidable. Finally, we give a finer analysis of the problem for particular classes of DTDs, exploring the impact of various DTD constructs, identifying tractable cases, as well as providing the complexity in the query size alone.

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Abstract-This paper investigates the discovery of conditional functional dependencies (CFDs). CFDs are a recent extension of functional dependencies (FDs) by supporting patterns of semantically related constants, and can be used as rules for cleaning relational data. However, finding CFDs is an expensive process that involves intensive manual effort. To effectively identify data cleaning rules, we develop techniques for discovering CFDs from sample relations. We provide three methods for CFD discovery. The first, referred to as CFDMiner, is based on techniques for mining closed itemsets, and is used to discover constant CFDs, namely, CFDs with constant patterns only. The other two algorithms are developed for discovering general CFDs. The first algorithm, referred to as CTANE, is a levelwise algorithm that extends TANE, a well-known algorithm for mining FDs. The other, referred to as FastCFD, is based on the depthfirst approach used in FastFD, a method for discovering FDs. However, for CFD-based cleaning methods to be effective in practice, it is necessary to have techniques in place that can automatically discover, profile, or learn CFDs from sample data, to be used as data cleaning rules. As indicated in [8], profiling of data cleaning rules is critical to commercial data quality tools.This practical concern highlights the need for studying the discovery problem for CFDs: given a sample instance r of a relation schema R, it is to find a canonical cover of all CFDs that hold on r, i.e., a set of CFDs that is logically equivalent to the set of all CFDs that hold on r. To reduce redundancy, each CFD in the canonical cover should be minimal, i.e., nontrivial and left-reduced (see [9] for nontrivial and left-reduced FDs).The discovery problem is, however, highly nontrivial. It is already hard for traditional FDs since, among other things, a canonical cover of FDs discovered from a relation r is inherently exponential in the arity of the schema of r, i.e., the number of attributes in R. Since CFD discovery subsumes FD

We study the satisfiability problem associated with XPath in the presence of DTDs. This is the problem of determining, given a query p in an XPath fragment and a DTD D, whether or not there exists an XML document T such that T conforms to D and the answer of p on T is nonempty. We consider a variety of XPath fragments widely used in practice, and investigate the impact of different XPath operators on satisfiability analysis. We first study the problem for negation-free XPath fragments with and without upward axes, recursion and data-value joins, identifying which factors lead to tractability and which to NP-completeness. We then turn to fragments with negation but without data values, establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion. We show that with negation the complexity ranges from PSPACE to EXPTIME. Moreover, when both data values and negation are in place, we find that the complexity ranges from NEXPTIME to undecidable. Finally, we give a finer analysis of the problem for particular classes of DTDs, exploring the impact of various DTD constructs, identifying tractable cases, as well as providing the complexity in the query size alone.

Abstract