Approximate dependencies in database systems

Functional dependencies are the most commonly used approach for capturing real-word integrity constraints which are to be reflected in a database. There are, however, many useful kinds of constraints, especially approximate ones, that cannot be represented correctly by functional dependencies and therefore are enforced via programs which update the database, if they are enforced at all. This tends to make such constraints invisible since they are not an explicit part of the database, increasing maintenance problems and the likelihood of inconsistencies. We propose a new approach, cluster dependencies, as a way to enforce approximate dependencies. By treating equality as a fuzzy concept and defining appropriate similarity measures, it is possible to represent a broad range of approximate constraints directly in the database by storing and accessing cluster definitions. We discuss different interpretations of cluster dependencies and describe the additional data structures needed to enforce them. We also contrast them with an existing approach, fuzzy functional dependencies, which are much more limited in the kind of approximate constraints they can represent.     

Mining functional dependencies from data

In this paper, we propose an efficient rule discovery algorithm, called FD_Mine, for mining functional dependencies from data. By exploiting Armstrong’s Axioms for functional dependencies, we identify equivalences among attributes, which can be used to reduce both the size of the dataset and the number of functional dependencies to be checked. We first describe four effective pruning rules that reduce the size of the search space. In particular, the number of functional dependencies to be checked is reduced by skipping the search for FDs that are logically implied by already discovered FDs. Then, we present the FD_Mine algorithm, which incorporates the four pruning rules into the mining process. We prove the correctness of FD_Mine, that is, we show that the pruning does not lead to the loss of useful information. We report the results of a series of experiments. These experiments show that the proposed algorithm is effective on 15 UCI datasets and synthetic data.     

On learning multivalued dependencies with queries

Data dependencies play an important role in the design of relational databases. There is a strong connection between dependencies and some fragments of the propositional logic. In particular, functional dependencies are closely related to Horn formulas. Also, multivalued dependencies are characterized in terms of multivalued formulas. It is known that both Horn formulas and sets of functional dependencies are learnable in the exact model of learning with queries. Here we present an algorithm that learns a non-trivial subclass of multivalued formulas using membership and equivalence queries. Furthermore, a slight modification of the algorithm allows us to learn the corresponding subclass of multivalued dependencies.     

XML函数依赖研究综述

函数依赖作为数据库规范化的基础在关系理论中起着重要的作用。近年来，XML得到广泛应用并已成为互联网上数据传输和交换的标准。由于XML半结构化的特性，使得如何定义XML函数依赖使其具有更强的描述能力，以及如何解决相应的逻辑蕴涵问题成为当今学术界所面临的挑战。针对这些问题，系统地描述了目前关于XML函数依赖的研究现状，特别是把分析的重点放在如何定义函数依赖、判断其蕴涵关系以及从XML文档中发现函数依赖等问题上。最后讨论了诸如类型化函数依赖关系等一些相关的研究方向。     

Negative results on learning multivalued dependencies with queries

Data dependencies are useful to design relational databases. There is a strong connection between dependencies and some fragments of the propositional logic. In particular, functional dependencies are closely related to Horn formulas. Also, multivalued dependencies are characterized in terms of multivalued formulas. It is known that both Horn formulas and sets of functional dependencies are learnable in the exact model of learning with queries. Here we proof that neither multivalued formulas nor multivalued dependencies can be learned using only membership queries or only equivalence queries.     

Deciding implication for functional dependencies in complex-value databases

Modern applications increasingly require the storage of data beyond relational structure. The challenge of providing well-founded data models that can handle complex objects such as lists, sets, multisets, unions and references has not been met yet in a completely satisfactory way. The success of such data models will greatly depend on the existence of automated database design techniques that generalise achievements from relational databases. In this paper, we study the implication problem of functional dependencies (FDs) in the presence of records, sets, multisets and lists. Database schemata are defined as nested attributes, database instances as nested relations and FDs are defined in terms of subattributes of the database schema. The expressiveness of FDs deviates fundamentally from previous approaches in different data models including the nested relational data model and XML.     

基于条件函数依赖的数据库一致性检测研究

条件函数依赖是函数依赖在语义上的扩充,可以应用于数据清洗工作,在数据库一致性的修复上应用广泛。讨论了条件函数依赖的相关语义规则,重点研究了基于条件函数依赖对违反数据库一致性元组的检测工作,并引入置信度评价机制,对相关的检测规则进行了改进。改进后的检测方法在基于多个函数依赖的检测中显示出了优越性,使得检测工作更为精简,检测标准更加明确。     

A note on approximation measures for multi-valued dependencies in relational databases

We consider the problem of defining a normalized approximation measure for multi-valued dependencies in relational database theory. An approximation measure is a function mapping relation instances to real numbers. The number to which an instance is mapped, intuitively, describes the strength of the dependency in that instance. A normalized approximation measure for functional dependencies has been proposed previously: the minimum number of tuples that need be removed for the functional dependency to hold divided by the total number of tuples. This leads naturally to a normalized measure for multi-valued dependencies: the minimum number of tuples that need be removed for the multi-valued dependency to hold divided by the total number of tuples.The measure for functional dependencies can be computed efficiently, O(|r|log(|r|)) where |r| is the relation instance. However, we show that an efficient algorithm for computing the analogous measure for multi-valued dependencies is not likely to exist. A polynomial time algorithm for computing the measure would lead to a polynomial time algorithm for an NP-complete problem (proven by a reduction from the maximum edge biclique problem in graph theory). Hence, we argue that it is not a good measure. We propose an alternate measure based on the lossless join characterization of multi-valued dependencies. This measure is efficiently computable, O(|r|²).     

Axiomatizing the Logical Core of XPath 2.0

The first aim of this paper is to present the logical core of XPath 2.0: a logically clean, decidable fragment, which includes most navigational features of XPath 2.0 (complex counting conditions and data joins are not supported, as they lead to undecidability). The second aim is to provide a list of equations completely axiomatizing query equivalence in this language (i.e., all other query equivalences can be derived from these). A preliminary version of this paper was published in the proceedings of ICDT 2007. We would like to thank Jan Hidders for pointing us to the interesting question of stronger forms of completeness (cf. Sect. 4.3). We would also like to thank the anonymous reviewers for their extensive comments, which have greatly improved the quality of the paper. The first author is supported by NWO grant 639.021.508.     

XML数据库计划的公理化演进

数据库计划是由它的实体之间的模式关系构成, 该计划随着时间的改变被称为计划演进。XML 数据库计划的公理化演进指的是当该计划产生根本的变动时, XML 数据库能自动维持其数据的完整性。提出的公理化模式为XML 数据库演进的问题提供了一个一般的解决方案, 它能明确地决定计划的修改行为和自动维持其数据的完整性。     

Nondeterministic dependencies in relations: An extention of the concept of functional dependency

In the present article, some special semantic integrity constraints—so called nondeterministic dependencies—are proposed. These dependencies can be regarded as stochastic extensions of functional dependencies. After some basic definitions, the concept of nondeterministic dependency is introduced. Examples are given and an implementation for a statistical analysis system is described. Some properties are discussed.     

Functional dependencies among Boolean dependencies

In this paper, we consider functional dependencies among Boolean dependencies (BDs, for short). Armstrong relations are defined for BDs (called BD-Armstrong relations). For BDs, two necessary and sufficient conditions for the existence of BD-Armstrong relations are given. A necessary and sufficient condition for the existence of Armstrong relations for functional dependencies (FDs, for short) is given, which in some sense is more convenient than the condition given in [3]. We give an algorithm that solves the problem of deciding if two BDs imply the same set of functional dependencies. If the BDs are given in perfect disjunctive normal form, then the algorithm requires only polynomial time. Although Mannila and Räihä have shown that for some relations exponential time is needed for computing any cover of the set of FDs defined in this relation, as a consequence, we show that the problem of deciding if two relations satisfy the same set of FDs can be solved in polynomial time. Another consequence is a new correspondence of the families of functional dependencies to the families of Sperner systems. By this correspondence, the estimate of the number of databases given previously in [6] is improved. It is shown that there is a one-to-one correspondence between the closure of the FDs that hold in a BD and its so-calledbasic cover. As applications of basic covers, we obtain a representation of a key, the family of minimal keys and a representation of canonical covers.This research was supported by the Hungarian Foundation for Scientific Research, Grant Nos. OTKA 2575, 2149.     

The theory of functional and subset dependencies over relational expressions

A formal system for reasoning about functional dependencies (FDs) and subset dependencies (SDs) defined over relational expressions is described. An FD e:X → Y indicates that Y is functionally dependent on X in the relation denoted by expression e; an SD e ? f indicates that the relation denoted by e is a subset of that denoted by f. The system is shown to be sound and complete by resorting to the analytic tableaux method. Applications of the system include the problem of determining if a constraint of a subschema is implied by the constraints of the base schema and the development of database design methodologies similar to normalization.     

Incorporating cardinality constraints and synonym rules into conditional functional dependencies

We propose an extension of conditional functional dependencies (CFDs), denoted by CFDcs, to express cardinality constraints, domain-specific conventions, and patterns of semantically related constants in a uniform constraint formalism. We show that despite the increased expressive power, the satisfiability and implication problems for CFDcs remain NP-complete and coNP-complete, respectively, the same as their counterparts for CFDs. We also identify tractable special cases.     

基于内容感知发现XML条件函数依赖

针对XML函数依赖(XFD)不能充分检测XML局部数据源语义上的数据不一致,借鉴关系数据库中条件函数依赖(CFD)的概念,并根据XML自身结构和约束特性,提出了基于内容感知发现(CAD)XML条件函数依赖(XCFD),CAD使用隐藏在数据值中的内容发现局部XML文档的XCFDs,检测异构数据源中数据一致性,提高数据的质量,并给出了详细的算法,同时引入修剪规则集减少搜索点阵和候选的XCFD的数量,提高算法的效率,使得XCFD无冗余、最小化.通过案例研究表明,基于CAD方法发现的XCFD比现有XFD发现更多的函数依赖和语义约束.     

粒计算支持的粗糙函数依赖的研究

利用粒计算方法对粗糙关系数据库（Rough Relational Database,RRDB）的粗糙函数依赖进行研究。首先提出了两种类型的粗糙函数依赖及粗糙相似关系的概念,分析了如何利用位模式表示粗糙关系的属性值,在此基础上给出了利用粒计算方法对粗糙关系的属性间的依赖关系的进行判定的算法,实验验证算法是有效可行的。     

Analysis of dependencies in advanced transaction models

Transactional dependencies play an important role in coordinating and executing the subtransactions in advanced transaction processing models, such as, nested transactions and workflow transactions. Researchers have formalized the notion of transactional dependencies and have shown how various advanced transaction models can be expressed using different kinds of dependencies. Incorrect specification of dependencies can result in unpredictable behavior of the advanced transaction, which, in turn, can lead to unavailability of resources and information integrity problems. In this work, we focus on how to correctly specify dependencies in an advanced transaction. We enumerate the different kinds of dependencies that may be present in an advanced transaction and classify them into two broad categories: event ordering and event enforcement dependencies. Different event ordering and event enforcement dependencies in an advanced transaction often interact in subtle ways resulting in conflicts and redundancies. We describe the different types of conflicts that can arise due to the presence of multiple dependencies and describe how one can detect such conflicts. An advanced transaction may also contain redundant dependencies—these are dependencies that can be logically derived from other dependencies. We show how such extraneous dependencies can be eliminated to get an equivalent set of dependencies that has the same effect as the original set. Our dependency analysis is done in the context of a generalized advanced transaction model that is capable of expressing different kinds of advanced transactions. Recommended by: Amit Sheth