Set Of Functional Dependencies Research Articles

Towards the efficient discovery of meaningful functional dependencies

We propose the first framework for discovering the set of meaningful functional dependencies from data. This set contains the true positives among the set of functional dependencies that hold on the given data. Based on new data structures and original techniques for the dynamic computation of stripped partitions, we devise a new hybridization strategy that results in the first algorithm that can explore trade-offs between runtime efficiency and main memory usage. Using real-world benchmark data, we demonstrate that our algorithm outperforms the previous state-of-the-art in terms of runtime efficiency, and scalability in the number of rows and columns. We propose the number of redundant data values for ranking the functional dependencies that have been discovered. Our ranking helps separate false from true positives for applications, such as schema design. The remaining meaningful functional dependencies consist of the false negatives, that is, those functional dependencies that are only violated by the given data due to data inconsistency. We propose the computation of informative Armstrong relations to draw the attention of users to violations of functional dependencies that are meaningful for some application. We order the pairs of records in Armstrong relations based on the amount of inconsistency and redundancy caused by the associated functional dependencies, thereby pointing the attention to those most likely to be meaningful. As we demonstrate, these samples help separate false from true negatives, their perfect recall of meaningful functional dependencies can lead to a more complete acquisition of requirements and identification of dirty data, and may be computed faster than covers of functional dependencies. In addition, we demonstrate for the first time that non-redundant covers can offer a representation of functional dependencies that is much smaller than left-hand side reduced covers used in previous work. Such a compact representation of the output is easier to understand and explore by humans. We report all our results for different interpretations of missing values.

Математичні методи скорочення простору аналізованих станів при обробці «великих даних»

This paper addresses the problem of creating mathematical methods to optimize time and computing resources when processing Big Data. These methods are based on the proposed data organizational structure called “m-tuples based on ordered sets of arbitrary cardinality”. We formulated certain properties of the given data organizational structure as a consequence of the logical rules applied for the formation of m-tuples. A set of functional dependencies was also derived between m-tuples based on their location in the structure. A graphical interpretation was presented to illustrate the change of dynamics in fractions of operand combinations for which one tuple is a subset of the other. It takes into account the variation in the lengths of operand tuples. We also obtained logical conclusions about the influence of the properties studied and mathematical methods of working with the given structure to minimize the computing resources involved.

Relational database schema design for uncertain data

Driven by the dominance of the relational model, we investigate how the requirements of applications on the certainty of functional dependencies can improve the outcomes of relational database schema design. For that purpose, we assume that tuples are assigned a degree of possibility with which they occur in a relation, and that functional dependencies are assigned a dual degree of certainty which says to which tuples they apply. A design theory is developed for functional dependencies with degrees of certainty, including efficient axiomatic and algorithmic characterizations of their implication problem. Naturally, the possibility degrees of tuples bring forward different degrees of data redundancy, caused by functional dependencies with the dual degree of certainty. Variants of the classical syntactic Boyce–Codd and Third Normal Forms are established. They are justified semantically in terms of eliminating data redundancy and update anomalies of given degrees, and minimizing data redundancy of given degrees across all dependency-preserving decompositions, respectively. As a practical outcome of our results, designers can simply fix the degree of certainty they target, and then apply classical decomposition and synthesis to the set of functional dependencies whose associated degree of certainty meets the target. Hence, by fixing the certainty degree a designer controls which integrity requirements will be enforced for the application and which data will be processed by the application. The choice of the certainty degree also balances the classical trade-off between query and update efficiency on future database instances. Our experiments confirm the effectiveness of our control parameter, and provide original insight into classical normalization strategies and their implementations.

Finding the Transitive Closure of Functional Dependencies using Strategic Port Graph Rewriting

We present a new approach to the logical design of relational databases, based on strategic port graph rewriting. We show how to model relational schemata as attributed port graphs and provide port graph rewriting rules to perform computations on functional dependencies. Using these rules we present a strategic graph program to find the transitive closure of a set of functional dependencies. This program is sound, complete and terminating, assuming that there are no cyclical dependencies in the schema.

Mind your dependencies for semantic query optimization

Semantic query optimization uses dependencies between attributes to formulate query transformations and revise the number of processed rows, with direct impact on performance. Commercial databases present facilities to define dependencies as not enforced constraints. The goal is to help the query optimizer in cases where the database is denormalized or simply lost dependencies in the design. However, feeding these facilities is a manual task which is tedious and error-prone. An attractive alternative is the automatic discovery of dependencies, but the cost of finding dependencies increases with the number of rows and attributes in the dataset. In this paper, we stick to the automatic discovery approach, but to reduce the cost we focus on dependencies matching the current queries in the pipe (ie., workload). Initially, we rely on a large set of functional dependencies computed in batch with state of the art algorithms in the literature. Over time our focused dependency selector (FDSel) chooses exemplars to feed the query optimizer. Therewith we eliminate further manual interactions. The automatically selected exemplars exhibit statistical properties that resemble those of the initial dependency set. This demonstrates the effectiveness of our proposed approach. In the best case scenario, by applying the FDSel for join elimination on a real-world database, we reduce query response time by more than one order of magnitude.

ON THE APPROACH TO SEARCHING FOR FUNCTIONAL DEPENDENCES OF DATA IN RELATIONAL SYSTEMS

The subject matter of the study is information systems built on the basis of relational databases. The goal of the article is to develop a method for re-engineering relational databases that takes into account implicit interrelated functionally dependent data that affect the structure of the logical model. The following results are obtained: the approach to identify previously unknown functional dependencies based on the analysis of a set of relational database data is suggested; the classes of tasks of reengineering relational databases are specified; the stage of developing the target logic diagram which is common for the problems of adaptation and refactoring was studied; the sub-task of checking if the logic diagram of the relational database corresponds to the third normal form within this stage is considered using the synthesis method; it is shown that the solution of this task involves a number of difficulties, in particular, it is necessary to find a set of functional dependencies that are performed on the current instance of the data of a relational database; the approach for finding a set of functional dependencies from an instance of the data of a relational structure is suggested. The direction of further research can be the support of empty values at the stage of identifying functional dependencies as well as the issues of data transfer without any loss from the initial structure of the database to the target data obtained as a result of applying the methods of re-engineering. Conclusions. The approach is suggested to identify previously unknown functional dependencies which are based on the analysis of a set of relational database data. The first step is to get a set of functional dependencies for each relationship. The similar operation for the universal relation of the target database is performed at the second step. At this step, functional dependencies among the attributes of different relationships, that is the interrelationships among the data that were established during the information system operation, can be identified. The method for determining their information novelty is suggested; this method consists in verifying the membership of the functional dependencies of the universal relation while discovering the union of sets of dependencies of individual relations. A promising direction for further research is the development of methods to implement the technology for verifying if the obtained dependencies correspond to the logical model of the domain.

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.

Efficient bottom-up Mining of Attribute Based Access Control Policies.

Attribute Based Access Control (ABAC) is fast replacing traditional access control models due to its dynamic nature, flexibility and scalability. ABAC is often used in collaborative environments. However, a major hurdle to deploying ABAC is to precisely configure the ABAC policy. In this paper, we present an ABAC mining approach that can automatically discover the appropriate ABAC policy rules. We first show that the ABAC mining problem is equivalent to identifying a set of functional dependencies in relational databases that cover all of the records in a table. We also propose a more efficient algorithm, called ABAC-SRM which discovers the most general policy rules from a set of candidate rules. We experimentally show that ABAC-SRM is accurate and significantly more efficient than the existing state of the art.

Về các phép mã hóa hợp lý

In process to implement a database scheme with “good” qualities, at the first step, we often assign to each of the set of entities a number (a code). Making note that almost the complexity of conceptual algorithms is usually, at least, proportional to number of codes of attributes, and to the length of the dependency set, we study methods are so-called “logical codings”. In this paper, we study logical codings on an universal U =<S,F>, in which S is the set of attributes, F is the set of functional dependencies. Those logical codings are to be proven independent to all conceptual algorithms. And at the final, we introduce the logical codings NGH which has low complexity and produces a minimal set of codes.

Directed hypergraphs: Introduction and fundamental algorithms—A survey

Just as ordinary hypergraphs are a generalization of graphs, directed hypergraphs (DH) are a natural generalization of digraphs. A DH consists of a set of vertices V and a set of hyperarcs H, where a hyperarc is a pair <S,v>, S non empty subset of V and v∈V. DHs have a variety of applications: they have been used to represent functional dependency in databases, Horn formulae in propositional logic, and–or graphs, context free grammars etc. In the paper, after providing a brief historical introduction on the notion of DH and some relevant applications, various problems regarding DHs are surveyed and analyzed. In particular we consider the complexity of the reachability problem (together with its application in the related satisfiability problem for Horn CNF formulae) and the computation of transitive closure and transitive reduction of directed hypergraphs (together with its application to the computation of minimum coverings for a set of functional dependencies). Finally a short introduction to the problem of computing shortest hyperpaths in directed hypergraphs is provided.

Learning Sets of Antecedent-restricted Functional and Multivalued Dependencies with Queries

Identifying dependencies that hold in relational databases is essential to produce good databases designs. In particular, functional and multivalued dependencies are used to obtain relation schemes that satisfy the 4th normal form, a property that is considered satisfactory for most applications. It is known that the class of sets of functional dependencies is learnable in the exact model of learning with queries. Also a subclass of multivalued dependencies, the class of consequent-restricted multivalued dependencies, has been shown to be learnable in this model. In this paper, we present an algorithm that learns a class that contains sets of both functional and multivalued dependencies under some restrictions imposed on the antecedents of dependencies. We also show, as a by-product, an algorithm that learns a non-trivial subclass of 2-quasi Horn formulas, closely related to the class just mentioned.

Learning an Extension of the Class of Functional Dependencies with Queries

Data dependencies are a useful tool to design relational databases. In particular, functional and multivalued dependencies are used to obtain relation schemes that satisfy the 4th normal form, a property that is considered good enough for most applications. It is known that the class of sets of functional dependencies is learnable in the exact model of learning with queries. Also a subclass of multivalued dependencies, the class of consequent-restricted multivalued dependencies has been shown to be learnable in this model. Here, we present an algorithm that learns a generalization of both classes. We also show an algorithm that learns a non-trivial subclass of 2-quasi Horn formulas, closely related to the classes mentioned above.

Research on Functional Dependency for XML Schema

In this paper, gives the concept of functional dependency for XML based on Tree Tuples, furthermore, infers a inference rules set of functional dependency by using Armstrong axiom-system of database system.

Automating the Lower and Higher Normal Form Process for the Database Systems

is an important technique for the analysis of relational databases. It aims to create a set of relational tables with minimum data redundancy that preserve consistency and facilitate correct insertion, deletion, and modification. It is very much time consuming to do this data analysis manually. Thus in this paper, a system is proposed which aims to automate the most complex phase of the database design normalization. It will help to achieve a good database design and eliminate the drawbacks of manual normalization process. This system is suitable to eliminate redundancy and inconsistent dependency automatically. It aims to handle the normalization process up to fifth normal. This includes creating tables and establishing relationships between those tables by using their general definitions in a step-by-step feature on the set of functional dependencies to remove redundant data. Then this system is tested on many examples with multiple candidate keys taken from different sources.

Certain query answering in partially consistent databases

A database is called uncertain if two or more tuples of the same relation are allowed to agree on their primary key. Intuitively, such tuples act as alternatives for each other. A repair (or possible world) of such uncertain database is obtained by selecting a maximal number of tuples without ever selecting two tuples of the same relation that agree on their primary key. For a Boolean queryq, the problem CERTAINTY(q) takes as input an uncertain databasedband asks whetherqevaluates to true on every repair ofdb.In recent years, the complexity of CERTAINTY(q) has been studied under different restrictions onq. These complexity studies have assumed no restrictions on the uncertain databases that are input to CERTAINTY(q). In practice, however, it may be known that these input databases are partially consistent, in the sense that they satisfy some dependencies (e.g., functional dependencies). In this article, we introduce the problem CERTAINTY(q) in the presence of a set Σ of dependencies. The problem CERTAINTY(q, Σ) takes as input an uncertain databasedbthat satisfiesΣ, and asks whether every repair ofdbsatisfiesq.We focus on the complexity of CERTAINTY(q, Σ) whenqis an acyclic conjunctive query without self-join, and Σ is a set of functional dependencies and join dependencies, the latter of a particular form. We provide an algorithm that, givenqand Σ, decides whether CERTAINTY(q, Σ) is first-order expressible. Moreover, we show how to effectively construct a first-order definition of CERTAINTY(q, Σ) if it exists.

ПРОГНОЗУВАННЯ ПОКАЗНИКІВ ПРОЕКТУ НА ОСНОВІ КОГНІТИВНОЇ МОДЕЛІ, ЩО ПРЕДСТАВЛЕНА ДВОДОЛЬНИМ ГРАФОМ

All existing methods of planning and monitoring of the project progress include the presence of clear analytical relationship between the project parameters. Due to the limited information in the absence of analytical relationships between the factors a problem of forecasting the parameters of the project in the course of time have been appeared. The concept of a prediction model based on the integration of the project mechanisms of cognitive modeling and underdetermined computational models as the most effective way of solving constraint satisfaction problems has been suggested. The four conditions of the possibility of integration models: equivalence of sets of factors, included a sets of functional dependencies, extensibility digraph to computational network and portability of computing mechanisms of cognitive modeling on the base of underdetermined computational models have been analyzed. It is shown that it is not only retains all the advantages of the first, but also eliminates a number of shortcomings. The feasibility of the proposed mechanism for solving the problems of project management has been given. The further steps on integration of cognitive modeling and underdetermined computational models have been determined.

On the distance of databases

In the present paper a distance concept of databases is investigated. Two database instances are of distance 0, if they have the same number of attributes and satisfy exactly the same set of functional dependencies. This naturally leads to the poset of closures as a model of changing database. The distance of two databases (closures) is defined to be the distance of the two closures in the Hasse diagram of that poset. We determine the diameter of the poset and show that the distance of two closures is equal to the natural lower bound, that is to the size of the symmetric difference of the collections of closed sets. We also investigate the diameter of the set of databases with a given system of keys. Sharp upper bounds are given in the case when the minimal keys are 2 (or r)-element sets.

Nonparametric Identification of LPV Models Under General Noise Conditions: An LS-SVM Based Approach

Parametric identification approaches in the Linear Parameter-Varying (LPV) setting require optimal prior selection of a set of functional dependencies, used in the parametrization of the model coefficients, to provide accurate model estimates of the underlying system. Consequently, data-driven estimation of these functional dependencies has a paramount importance, especially when very limited a priori knowledge is available. Existing overparametrization and nonparametric methods dedicated to nonlinear estimation offer interesting starting points for this problem, but need reformulation to be applied in the LPV setting. Moreover, most of these approaches are developed under quite restrictive auto-regressive noise assumptions. In this paper, a nonparametric Least-Squares Support Vector Machine (LS-SVM) approach is extended for the identification of LPV polynomial models. The efficiency of the approach in the considered noise setting is shown, but the drawback of the auto-regressive noise assumption is also demonstrated by a challenging LPV identification example. To preserve the attractive properties of the approach, but to overcome the drawbacks in the estimation of polynomial LPV models in a general noise setting, a recently developed Instrumental Variable (IV)-based extension of the LS-SVM method is applied. The performance of the introduced IV and the original LS-SVM approaches are compared in an identification study of an LPV system with unknown noise dynamics.

An incremental approach for maintaining functional dependencies

A general assumption in all existing algorithms permitting to mine functional dependencies is that the database is static. However, real life databases are frequently updated. To the best of our knowledge, the discovery of functional dependencies in dynamic databases has never been studied. A naive solution consists in re-applying one of the existing algorithms to discover functional dependencies holding on the updated database. Nevertheless, in many domains, where response time is crucial, re-executing algorithms from scratch would be inacceptable. In this paper, we propose a new technique that makes use of the previously discovered results to cut down the amount of work that has been done to discover the new set of functional dependencies satisfied by the updated database.

Cover of the set of functional dependencies and quasinorms in database model if block

Cover of the set of functional dependencies and quasinorms in database model if block