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]: To accurately match records it is often necessary to utilize the semantics of the data. Functional dependencies (FDs) have proven useful in identifying tuples in a clean relation, based on the semantics of the data. For all the reasons that FDs and their inference are needed, it is also important to develop dependencies and their reasoning techniques for matching tuples from unreliable data sources. This paper investigates dependencies and their reasoning for record matching. (a) We introduce a class of matching dependencies (MDs) for specifying the semantics of data in unreliable relations, defined in terms of similarity metrics and a dynamic semantics. (b) We identify a special case of MDs, referred to as relative candidate keys (RCKs), to determine what attributes to compare and how to compare them when matching records across possibly different relations. (c) We propose a mechanism for inferring MDs, a departure from traditional implication analysis, such that when we cannot match records by comparing attributes that contain errors, we may still find matches by using other, more reliable attributes. (d) We provide an O(n2) time algorithm for inferring MDs, and an effective algorithm for deducing a set of RCKs from MDs. (e) We experimentally verify that the algorithms help matching tools efficiently identify keys at compile time for matching, blocking or windowing, and that the techniques effectively improve both the quality and efficiency of various record matching methods.

[2]: Often, in the real world, entities have two or more representations in databases. Duplicate records do not share a common key and or they contain errors that make duplicate matching a difficult task. Errors are introduced as the result of transcription errors, incomplete information, lack of standard formats, or any combination of these factors. In this paper, we present a thorough analysis of the literature on duplicate record detection. We cover similarity metrics that are commonly used to detect similar field entries, and we present an extensive set of duplicate detection algorithms that can detect approximately duplicate records in a database. We also cover multiple techniques for improving the efficiency and scalability of approximate duplicate detection algorithms. We conclude with coverage of existing tools and with a brief discussion of the big open problems in the area

[3]: Dependency theory is almost as old as relational databases themselves, and has traditionally been used to improve the quality of schema, among other things. Recently there has been renewed interest in dependencies for improving the quality of data. The increasing demand for data quality technology has also motivated revisions of classical dependencies, to capture more inconsistencies in real-life data, and to match, repair and query the inconsistent data. This paper aims to provide an overview of recent advances in revising classical dependencies for improving data quality.

[4]: When merging data from various sources, it is often the case that small variations in data format and interpretation cause traditional functional dependencies (FDs) to be violated, without there being an intrinsic violation of semantics. Examples include differing address formats, or different reported latitude longitudes for a given address. In this paper, we define metric functional dependencies, which strictly generalize traditional FDs by allowing small differences (controlled by a metric) in values of the consequent attribute of an FD. We present efficient algorithms for the verification problem: determining whether a given metric FD holds for a given relation. We experimentally demonstrate the validity and efficiency of our approach on various data sets that lie in multidimensional spaces.
The concept of matching dependencies ( ) is first proposed in [3] for specifying matching rules for the object identification (see [2] for a survey). The can be regarded as a generalization of , which are based on identical values having matching similarity equal to @math exactly. Thus, can be represented by the syntax of as well. For any two tuples, if their @math values are identical (with similarity threshold @math ), then a @math requires that their @math values are identical too, i.e., a @math . [4] also study the dependencies with matching similarities on attributes @math when given the matched values on @math , which can be treated as a special case of . The reasoning mechanism for deducing from a set of given is studied in [1] . The and their reason techniques can improve both the quality and efficiency of various record matching methods.