Controlling FD and MVD inferences in multilevel relational databasesystems

The authors investigate the inference problems due to functional dependencies (FD) and multivalued dependencies (MVD) in a multilevel relational database (MDB) with attribute and record classification schemes, respectively. The set of functional dependencies to be taken into account in order to prevent FD-compromises is determined. It is proven that incurring minimum information loss to prevent compromises is an NP-complete problem. An exact algorithm to adjust the attribute levels so that no compromise due to functional dependencies occurs is given. Some necessary and sufficient conditions for MVD-compromises are presented. The set of MVDs to be taken into account for controlling inferences is determined. An algorithm to prevent MVD-compromises in a relation with conflict-free MVDs is given     

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.     

A parallel algorithm for relational database normalization

The problem of database normalization in a parallel environment is examined. Generating relation schemes in third normal form is straightforward when given a set of functional dependencies that is a reduced cover. It is shown that a reduced cover for a set of functional dependencies can be produced in parallel. The correctness of the algorithm is based on two important theorems. it is demonstrated that the companion third normal form algorithm can be easily translated into a parallel version. The performance of the two algorithms is compared to the performance of their serial counterparts. The standard serial algorithms for computing minimal covers and synthesizing third normal form relations are presented. The parallel algorithms and their rationale are discussed     

外部闭包及其在关系数据库中的应用

本文引入了广义ＦＤ路和外部闭包的概念，将它们应用于函数依赖集的无冗余覆盖计算，有效地减少了计算的闭包个数．并在此基础上提出了一个新的３ＮＦ合成算法，将常用的３ＮＦ合成算法中的２次无冗余覆盖计算合并为１次，显著地减少了计算闭包总个数．     

基于模式图的规范化XML模式设计

在给定关系模式的属性集及其函数依赖最小覆盖集的基础上,提出一种基于模式图的规范化XML模式设计方法。定义了模式图,在模式图中增加了Keys的描述信息,给出由函数依赖集构造模式图的算法。该模式图独立于具体的XML模式语言,经分析证明,所设计的模式满足XNF。     

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.     

Propagating XML constraints to relations

We present a technique for refining the design of relational storage for XML data. The technique is based on XML key propagation: given a set of keys on XML data and a mapping (transformation) from the XML data to relations, what functional dependencies must hold on the relations produced by the mapping? With the functional dependencies one can then convert the relational design into, e.g. 3NF, BCNF, and thus develop efficient relational storage for XML data. We provide several algorithms for computing XML key propagation. One algorithm is to check whether a functional dependency is propagated from a set of XML keys via a predefined mapping; this allows one to determine whether or not the relational design is in a normal form. The others are to compute a minimum cover for all functional dependencies that are propagated from a set of XML keys and hold on a universal relation; these provide guidance for how to design a relational schema for storing XML data. These algorithms show that XML key propagation and its associated minimum cover can be computed in polynomial time. Our experimental results verify that these algorithms are efficient in practice. We also investigate the complexity of propagating other XML constraints to relations. The ability to compute XML key propagation is a first step toward establishing a connection between XML data and its relational representation at the semantic level.     

Inferring dependencies from relations: a conceptual clustering approach

In this paper we consider two related types of data dependencies that can hold in a relation: conjunctive implication rules between attribute‐value pairs, and functional dependencies. We present a conceptual clustering approach that can be used, with some small modifications, for inferring a cover for both types of dependencies. The approach consists of two steps. First, a particular clustered representation of the relation, called concept (or Galois ) lattice , is built. Then, a cover is extracted from the lattice built in the earlier step. Our main emphasis is on the second step. We study the computational complexity of the proposed approach and present an experimental comparison with other methods that confirms its validity. The results of the experiments show that our algorithm for extracting implication rules from concept lattices clearly outperforms an earlier algorithm, and suggest that the overall lattice‐based approach to inferring functional dependencies from relations can be seen as an alternative to traditional methods.     

分布式大数据函数依赖发现

在关系数据库中,函数依赖发现是一种十分重要的数据库分析技术,在知识发现、数据库语义分析、数据质量评估以及数据库设计等领域有着广泛的应用.现有的函数依赖发现算法主要针对集中式数据,通常仅适用于数据规模比较小的情况.在大数据背景下,分布式环境函数依赖发现更富有挑战性.提出了一种分布式环境下大数据的函数依赖发现算法,其基本思想是首先在各个节点利用本地数据并行进行函数依赖发现,基于以上发现的结果对函数依赖候选集进行剪枝,然后进一步利用函数依赖的左部(left hand side, LHS)的特征,对函数依赖候选集进行分组,针对每一组候选函数依赖并行执行分布式环境发现算法,最终得到所有函数依赖.对不同分组情况下所能检测的候选函数依赖数量进行了分析,在算法的执行过程中,综合考虑了数据迁移量和负载均衡的问题.在真实的大数据集上的实验表明,提出的检测算法在检测效率方面与已有方法相比有明显的提升.     

FD集最优覆盖多项式时间求解算法的研究

本文在详细分析了ＦＤ集的最小覆盖和最优覆盖的结构特性基础上，提出并讨论了一个最小覆盖成为最优覆盖的条件及一个最优覆盖珠属性集构成的特点，相应的引理和定理。最后给出一个求ＦＤ集最优覆盖的多项式时间算法。     

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).     

XML schema refinement through redundancy detection and normalization

As XML becomes increasingly popular, XML schema design has become an increasingly important issue. One of the central objectives of good schema design is to avoid data redundancies: redundantly stored information can lead not just only to a higher data storage cost but also to increased costs for data transfer and data manipulation. Furthermore, such data redundancies can lead to potential update anomalies, rendering the database inconsistent. One strategy to avoid data redundancies is to design redundancy-free schema from the start on the basis of known functional dependencies. We observe that XML databases are often “casually designed” and XML FDs may not be determined in advance. Under such circumstances, discovering XML data redundancies from the data itself becomes necessary and is an integral part of the schema refinement (or re-design) process. We present the design and implementation of the first system, DiscoverXFD, for efficient discovery of XML data redundancies. It employs a novel XML data structure and introduces a new class of partition-based algorithms. The XML data redundancies are defined on the basis of a new notion of XML functional dependency (XML FD) that (1) extends previous notions by incorporating set elements into the XML FD specification, and (2) maintains tuple-based semantics through the novel concept of Generalized Tree Tuple (GTT). Using this comprehensive XML FD notion, we introduce a new normal form (GTT-XNF) for XML documents, and provide comprehensive comparisons with previous studies. Given the set of data redundancies (in the form of redundancy-indicating XML FDs) discovered by DiscoverXFD, we describe a normalization algorithm for converting any original XML schema into one in GTT-XNF.     

Constraint Retraction in CLP(FD): Formal Framework and Performance Results

Constraint retraction can be described, in general, as the possibility of deleting a previously stated piece of information. This is obviously very convenient in many programming frameworks, especially in those that involve some level of interaction between the user and the system, or also in those concerning rescheduling or replanning. Nevertheless, constraint retraction is usually not provided in current constraint programming environments. This is mainly due to its high complexity and also to its non-monotonic nature, which would make most of such systems much more complex to reason with. In this paper we avoid these problems by considering a specific constraint programming framework, called clpFD, that is, constraint logic programming (CLP) over finite domain (FD) constraints. We propose an algorithm which deletes a constraint from a set of FD constraints, while maintaining partial arc-consistency, which is usual in this programming framework. What is crucial is that the retraction operation we propose is incremental, in that it follows the chain of dependencies among variables which are set by the nature of the FD constraints, and by doing so it updates only the part of the constraint set which is affected by the deletion. We also detail how constraint retraction can be incorporated in the FD constraint solver and we evaluate its behavior within the clpFD system. Experimental results on usual benchmarks, on classes of problems of increasing connectivity, and also on a real-life problem show that in almost all cases the use of our retraction algorithm provides great speed-up with respect to standard methods while not slowing down the clpFD system when no retraction is performed. This provides the system with an efficient way of retracting constraints while not changing its performance when the user does not want to use this new feature.     

Decomposition for a new kind of imprecise information system

In this paper, we first propose a new kind of imprecise information system, in which there exist conjunctions (∧’s), disjunctions (∨’s) or negations (¬’s). Second, this paper discusses the relation that only contains ∧’s based on relational database theory, and gives the syntactic and semantic interpretation for ∧ and the definitions of decomposition and composition and so on. Then, we prove that there exists a kind of decomposition such that if a relation satisfies some property then it can be decomposed into a group of classical relations (relations do not contain ∧) that satisfy a set of functional dependencies and the original relation can be synthesized from this group of classical relations. Meanwhile, this paper proves the soundness theorem and the completeness theorem for this decomposition. Consequently, a relation containing ∧’s can be equivalently transformed into a group of classical relations that satisfy a set of functional dependencies. Finally, we give the definition that a relation containing ∧’s satisfies a set of functional dependencies. Therefore, we can introduce other classical relational database theories to discuss this kind of relation.     

Computing unique canonical covers for simple FDs via transitive reduction

Although there is a rich body of research on dependency theory, only few results concerning simple functional dependencies (FDs) have been published. In this paper, the following key results regarding simple FDs are shown. First, given an acyclic set F of simple FDs there exists exactly one canonical cover for F. Second, this uniquely determined canonical cover can be computed via transitive reduction. Third, it is shown how a uniquely determined canonical cover can be fixed in case of arbitrary simple FDs via transitive reduction.     

LR最小替换集求解算法研究

文中对Ｄ．Ｍａｉｅｒ提出的关于关系数据库中的ＬＲ最小集的结构进行了分析，提出了一个比“ＬＲ最小集”更为简化的ＦＤ集的覆盖－ＬＲ最小替换集。给出了一个求ＬＲ最小替换集的多项式时间算法。修正了Ｄ．Ｍａｉｅｒ在其文中给出的一个ＦＤ集为最优覆盖的必要条件。     

基于蜂窝结构的传感器网络覆盖问题求解算法

在无线传感器网络中,求解能够完全覆盖目标区域的最小覆盖集是个NP难问题.在传感器节点数目较多时,目前只能通过近似算法求解.蜂窝结构是覆盖二维平面的最佳拓扑结构,但不能直接用于求解无线传感器网络的覆盖问题.提出了一种基于蜂窝结构的覆盖问题求解算法,在该算法迭代求解过程的每一阶段,选出一个节点加入到初始为空的节点集合中,并使得该节点集合的拓扑结构接近于蜂窝结构,直至该节点集合成为覆盖集.该算法在最坏情况下的时间复杂度为O(n3),这里n为传感器节点总数.实验结果表明该算法可在很短的时间内执行完,在所得覆盖集的大小方面要优于现有的覆盖问题求解算法.     

Towards an abstract theory of dependency constraints in relational databases

We introduce the notion of an FD system on a semilattice as a generalization of the concept of a closed set of functional dependencies, and we study lattice-theoretical properties of those objects. The notion of a table as an abstraction of relations of relational databases is also considered, and a generalization of relational algebra is presented; this offers a better perspective on the role played by Armstrong's relations. Finally, an application of this algebraic approach to dynamic databases is included.     

函数依赖推理控制的方法

文章研究了在多级安全数据库系统中由于函数依赖(FD)引起的推理问题,分析了Su和Ozsoyolu提出的CLA算法存在的问题,在此基础上,提出了一个递归的最小信息丢失分层密级调整算法,并分析了算法的时间复杂度。