You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality applications such as violation detection. In this paper, we study the problem of discovering matching dependencies from a given database instance. First, we formally define the measures, support and confidence, for evaluating utility of mds in the given database instance. Then, we study the discovery of mds with certain utility requirements of support and confidence. Exact algorithms are developed, together with pruning strategies to improve the time performance. Since the exact algorithm has to traverse all the data during the computation, we propose an approximate solution which only use some of the data. A bound of relative errors introduced by the approximation is also developed. Finally, our experimental evaluation demonstrates the efficiency of the proposed methods.

Cited Abstract(s):
[1]: This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.

[2]: The notion of roll-up dependency (RUD) extends functional dependencies with generalization hierarchies. RUDs can be applied in OLAP and database design. The problem of discovering RUDs in large databases is at the center of this paper. An algorithm is provided that relies on a number of theoretical results. The algorithm has been implemented; results on two real-life datasets are given. The extension of functional dependency (FD) with roll-ups turns out to capture meaningful rules that are outside the scope of classical FD mining. Performance figures show that RUDs can be discovered in linear time in the number of tuples of the input dataset.

[3]: The functional dependency inference problem is the following. Given a relation r, find a set of functional dependencies that is equivalent with the set of all functional dependencies holding in r. All known algorithms for this task have running times that can be in the worst case exponential in the size of the smallest cover of the dependency set. We consider approximate dependency inference. We define various measures for the error of a dependency in a relation. These error measures have the value 0 if the dependency holds and a value close to 1 if the dependency clearly does not hold. Depending on the measure used, all dependencies with error at least e in r can be detected with high probability by considering only O(1 e) or O(|r| 1 2 e) random tuples of r. We also show how a machine learning algorithm due to can be applied to give in output-polynomial time an approximately correct cover for the set of dependencies holding in r.

[4]: 

[5]: Dirty data is a serious problem for businesses leading to incorrect decision making, inefficient daily operations, and ultimately wasting both time and money. Dirty data often arises when domain constraints and business rules, meant to preserve data consistency and accuracy, are enforced incompletely or not at all in application code. In this work, we propose a new data-driven tool that can be used within an organization's data quality management process to suggest possible rules, and to identify conformant and non-conformant records. Data quality rules are known to be contextual, so we focus on the discovery of context-dependent rules. Specifically, we search for conditional functional dependencies (CFDs), that is, functional dependencies that hold only over a portion of the data. The output of our tool is a set of functional dependencies together with the context in which they hold (for example, a rule that states for CS graduate courses, the course number and term functionally determines the room and instructor). Since the input to our tool will likely be a dirty database, we also search for CFDs that almost hold. We return these rules together with the non-conformant records (as these are potentially dirty records). We present effective algorithms for discovering CFDs and dirty values in a data instance. Our discovery algorithm searches for minimal CFDs among the data values and prunes redundant candidates. No universal objective measures of data quality or data quality rules are known. Hence, to avoid returning an unnecessarily large number of CFDs and only those that are most interesting, we evaluate a set of interest metrics and present comparative results using real datasets. We also present an experimental study showing the scalability of our techniques.

[6]: We are given a large database of customer transactions. Each transaction consists of items purchased by a customer in a visit. We present an efficient algorithm that generates all significant association rules between items in the database. The algorithm incorporates buffer management and novel estimation and pruning techniques. We also present results of applying this algorithm to sales data obtained from a large retailing company, which shows the effectiveness of the algorithm.

[7]: The discovery of functional dependencies from relations is an important database analysis technique. We present TANE, an efficient algorithm for finding functional dependencies from large databases. TANE is based on partitioning the set of rows with respect to their attribute values, which makes testing the validity of functional dependencies fast even for a large number of tuples. The use of partitions also makes the discovery of approximate functional dependencies easy and efficient and the erroneous or exceptional rows can be identified easily. Experiments show that T ANE is fast in practice. For benchmark databases the running times are improved by several orders of magnitude over previously published results. The algorithm is also applicable to much larger datasets than the previous methods.

[8]: Conditional functional dependencies (CFDs) have recently been proposed as a useful integrity constraint to summarize data semantics and identify data inconsistencies. A CFD augments a functional dependency (FD) with a pattern tableau that defines the context (i.e., the subset of tuples) in which the underlying FD holds. While many aspects of CFDs have been studied, including static analysis and detecting and repairing violations, there has not been prior work on generating pattern tableaux, which is critical to realize the full potential of CFDs. This paper is the first to formally characterize a "good" pattern tableau, based on naturally desirable properties of support, confidence and parsimony. We show that the problem of generating an optimal tableau for a given FD is NP-complete but can be approximated in polynomial time via a greedy algorithm. For large data sets, we propose an "on-demand" algorithm providing the same approximation bound, that outperforms the basic greedy algorithm in running time by an order of magnitude. For ordered attributes, we propose the range tableau as a generalization of a pattern tableau, which can achieve even more parsimony. The effectiveness and efficiency of our techniques are experimentally demonstrated on real data.

[9]: 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. It leverages closed-itemset mining to reduce search space. Our experimental results demonstrate the following. (a) CFDMiner can be multiple orders of magnitude faster than CTANE and FastCFD for constant CFD discovery. (b) CTANE works well when a given sample relation is large, but it does not scale well with the arity of the relation. (c) FastCFD is far more efficient than CTANE when the arity of the relation is large.
The confidence and support measures are widely used in discovering approximate functional dependencies [7] [1] and evaluating [8] [5] [9] . The confidence can be interpreted as an estimate of the probability that a randomly drawn pair of tuples agreeing on @math also agree on @math [3] [2] . Scheffer [4] study the trade off between support and confidence for finding association rules [6] , by computing a expected prediction accuracy. In addition, Chiang and Miller [5] also study some other measures such as conviction and @math -test for evaluating dependency rules. When a candidate @math is suggested together with minimum support and confidence, [8] study the discovery of optimal with the minimum pattern tableau size. A concise set of patterns are naturally desirable which may have lower cost during the applications such as violation detection by . On the other hand, Chiang and Miller [5] explore by considering all the possible dependency candidates when @math is not specified. [9] , also study the case when the embedded are not given, and propose three algorithms for different scenarios.