Relaxing constraints in enhanced entity-relationship models using fuzzy quantifiers

While various articles about fuzzy entity relationship (ER) and enhanced entity relationship (EER) models have recently been published, not all examine how the constraints expressed in the model may be relaxed. In this paper, our aim is to relax the constraints which can be expressed in a conceptual model using the modeling tool, so that these constraints can be made more flexible. We will also study new constraints that are not considered in classic EER models. We use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and fuzzy query systems for databases. In addition, we shall examine the representation of these constraints in an EER model and their practical repercussions. The following constraints are studied: the fuzzy participation constraint, the fuzzy cardinality constraint, the fuzzy completeness constraint to represent classes and subclasses, the fuzzy cardinality constraint on overlapping specializations, fuzzy disjoint and fuzzy overlapping constraints on specializations, fuzzy attribute-defined specializations, fuzzy constraints in union types or categories and fuzzy constraints in shared subclasses. We shall also demonstrate how fuzzy (min, max) notation can substitute the fuzzy cardinality constraint but not the fuzzy participation constraint. All these fuzzy constraints have a new meaning, they offer greater expressiveness in conceptual design, and are included in the so-called fuzzy EER model.     

Cardinal: A Finite Sets Constraint Solver

In this paper we present Cardinal, a general finite sets constraint solver just made publicly available in ECLiPSe Constraint System, suitable for combinatorial problem solving by exploiting inferences over sets cardinality. In fact, to deal with set variables and set constraints, existing set constraint solvers are not adequate to handle a number of problems, as they do not actively use important information about the cardinality of the sets, a key feature in such problems. Cardinal is formally presented as a set of rewriting rules on a constraint store and we illustrate its efficiency with experimental results. We show the importance of propagating constraints on sets cardinality, by comparing Cardinal with other solvers. Another contribution of this paper is on modelling: we focus essentially on digital circuits problems, for which we present new modelling approaches and prove that sets alone can be used to model these problems in a clean manner and solve them efficiently using Cardinal. Results on a set of diagnostic problems show that Cardinal obtains a speed up of about two orders of magnitude over Conjunto, a previous available set constraint solver, which uses a more limited amount of constraint propagation on cardinalities. Additionally, to further extend modelling capabilities and efficiency, we generalized Cardinal to actively consider constraints over set functions other than cardinality. The Cardinal version just released allows declaring union, minimum and maximum functions on set variables, and easily constraining those functions, letting Cardinal especial inferences efficiently take care of different problems. We describe such extensions and discuss its potentialities, which promise interesting research directions.     

Nicolog: A simple yet powerful cc(FD) language

In this paper, we describe Nicolog, a language with capabilities similar to recently developed constraint logic programming (CLP) languages such as CLP(BNR), clp(FD), and cc(FD). Central to Nicolog are projection constraints (PCs), a sublanguage for compiling and optimizing constraint propagation in numeric and Boolean domains. PCs are an interesting generalization of the indexical constraints introduced in cc(FD) and also found in clp(FD). Nicolog compiles a very general class of built-in constraints into equivalent sets of PCs, allowing an arbitrary mixture of integer (easily extensible to real) and Boolean operations. Nicolog also lets the user program PCs directly, making it possible to implement new sophisticated propagation procedures. We show that PCs are a simple, efficient, and flexible way to implement most of the propagation procedures possible in other FD CLP systems. These include procedures for cardinality, constructive disjunction, implication, and mixed Boolean/numeric constraints. Empirical results with a simple prototype Nicolog implementation based on the WAM architecture show it can solve hard problems with speed comparable to the fastest existing CLP systems.     

Cardinality constraints in semantic data models

Constraints are central to the notion of a semantic data model. How well a model captures constraints affects its power and viability as a semantic data model. Cardinality constraints are an important subclass of general constraints. In this paper we provide formal definitions for cardinality constraints of several semantic models, as described in the literature. We construct a partial ordering of these constraints that shows the relative power expressed by each cardinality constraints. We discuss our results and offer possible extensions to contemporary cardinality constraint definitions. Our contributions include a collection and formal definition of existing cardinality constraints, a partial ordering of this set, and recommendations for cardinality constraint mechanisms in semantic data models.     

Global and local scatter based semi-supervised dimensionality reduction with active constraints selection in ensemble subspaces

Semi-supervised dimensionality reduction has attracted an increasing amount of attention in this big-data era. Many algorithms have been developed with a small number of pairwise constraints to achieve performances comparable to those of fully supervised methods. However, one challenging problem with semi-supervised approaches is the appropriate choice of the constraint set, including the cardinality and the composition of the constraint set which, to a large extent, affects the performance of the resulting algorithm. In this work, we address the problem by incorporating ensemble subspaces and active learning into dimensionality reduction and propose a new global and local scatter based semi-supervised dimensionality reduction method with active constraints selection. Unlike traditional methods that select the supervised information in one subspace, we pick up pairwise constraints in ensemble subspaces, where a novel active learning algorithm is designed with both exploration and filtering to generate informative pairwise constraints. The automatic constraint selection approach proposed in this paper can be generalized to be used with all constraint-based semi-supervised learning algorithms. Comparative experiments are conducted on four face database and the results validate the effectiveness of the proposed method.     

Maintenance of implication integrity constraints under updates to constraints

Semantic integrity constraints are used for enforcing the integrity of the database as well as for improving the efficiency of the database utilization. Although semantic integrity constraints are usually much more static as compared to the data itself, changes in the data semantics may necessitate corresponding changes in the constraint base. In this paper we address the problems related with maintaining a consistent and non-redundant set of constraints satisfied by the database in the case of updates to the constraint base. We consider implication constraints as semantic integrity constraints. The constraints are represented as conjunctions of inequalities. We present a methodology to determine whether a constraint is redundant or contradictory with respect to a set of constraints. The methodology is based on the partitioning of the constraint base which improves the efficiency of algorithms that check whether a constraint is redundant or contradictory with respect to a constraint base. Received August 19, 1993 / Accepted July 7, 1997     

A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

In the current work, a solution methodology which combines a meta-heuristic algorithm with an exact solution approach is presented to solve cardinality constrained portfolio optimization (CCPO) problem. The proposed method is comprised of two levels, namely, stock selection and proportion determination. In stock selection level, a greedy randomized adaptive search procedure (GRASP) is developed. Once the stocks are selected the problem reduces to a quadratic programming problem. As GRASP ensures cardinality constraints by selecting predetermined number of stocks and quadratic programming model ensures the remaining problem constraints, no further constraint handling procedures are required. On the other hand, as the problem is decomposed into two sub-problems, total computational burden on the algorithm is considerably reduced. Furthermore, the performance of the proposed algorithm is evaluated by using benchmark data sets available in the OR Library. Computational results reveal that the proposed algorithm is competitive with the state of the art algorithms in the related literature.     

Tractable cases of the extended global cardinality constraint

We study the consistency and domain consistency problem for extended global cardinality (EGC) constraints. An EGC constraint consists of a set X of variables, a set D of values, a domain D(x) í DD(x) \subseteq D for each variable x, and a “cardinality set” K(d) of non-negative integers for each value d. The problem is to instantiate each variable x with a value in D(x) such that for each value d, the number of variables instantiated with d belongs to the cardinality set K(d). It is known that this problem is NP-complete in general, but solvable in polynomial time if all cardinality sets are intervals. First we pinpoint connections between EGC constraints and general factors in graphs. This allows us to extend the known polynomial-time case to certain non-interval cardinality sets. Second we consider EGC constraints under restrictions in terms of the treewidth of the value graph (the bipartite graph representing variable-value pairs) and the cardinality-width (the largest integer occurring in the cardinality sets). We show that EGC constraints can be solved in polynomial time for instances of bounded treewidth, where the order of the polynomial depends on the treewidth. We show that (subject to the complexity theoretic assumption  FPT ≠ W[1]) this dependency cannot be avoided without imposing additional restrictions. If, however, also the cardinality-width is bounded, this dependency gets removed and EGC constraints can be solved in linear time.     

Null Inclusion Dependencies in Relational Databases

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. We introduce null inclusion dependencies (NINDs) to cater for the situation when a database is incomplete and contains null values. We show that the implication problem for NINDs is the same as that for INDs. We then present a sound and complete axiom system for null functional dependencies (NFDs) and NINDs, and prove that the implication problem for NFDs and NINDs is decidable and EXPTIME-complete. By contrast, when no nulls are allowed, this implication problem is undecidable. This undecidability result has motivated several researchers to restrict their attention to FDs and noncircular INDs in which case the implication problem was shown to be EXPTIME- complete. Our results imply that when considering nulls in relational database design we need not assume that NINDs are noncircular.     

Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint

Two Ant Colony Optimization algorithms are proposed to tackle multiobjective structural optimization problems with an additional constraint. A cardinality constraint is introduced in order to limit the number of distinct values of the design variables appearing in any candidate solution. Such constraint is directly enforced when an ant builds a candidate solution, while the other mechanical constraints are handled by means of an adaptive penalty method (APM). The test-problems are composed by structural optimization problems with discrete design variables, and the objectives are to minimize both the structure’s weight and its maximum nodal displacement. The Pareto sets generated in the computational experiments are evaluated by means of performance metrics, and the obtained designs are also compared with solutions available from single-objective studies in the literature.     

带有稀疏执行器故障的事件触发网络化系统容错控制

针对一类具有事件触发信息传输机制的网络化控制系统,对系统故障执行器个数进行稀疏约束,研究系统在有限个执行器失效情况下的指数稳定及控制器设计问题。将系统故障执行器个数的约束转化为对控制器增益矩阵行的势约束,利用混合整数方法来解决这类稀疏约束的容错控制问题。在此基础上,利用Lyapunov泛函方法,得出闭环系统在有限个执行器失效情况下系统呈指数稳定的充分条件以及具有行稀疏约束的控制器设计方法。最后,通过一个飞行控制系统的数值仿真实例验证所提控制方法的可行性和有效性。     

A sound and complete chase procedure for constrained tuple-generating dependencies

We present a chase procedure for solving the implication problem of constrained tuple-generating dependencies (ctgds), a general class of database dependencies that is also able to handle data and predicates on interpreted domains. Current chase procedures for ctgds are sound but not complete, in the sense that they are unguaranteed to stop successfully whenever implication is true. The procedure we present is sound and complete, the first to our knowledge. It follows a linear reasoning over constraint domains that have the Independence of Negative Constraints property. We then soundly extend this procedure by a disjunctive reasoning over unrestricted constraint domains. To achieve these results, we used a different approach. Previous chases act like a closure operator, whereas we used a goal-directed design.     

Constraint analysis: a design process for specifying operations onobjects

A design process for an object-oriented database design environment, known as constraint analysis, is presented. Given the increased level of semantics associated with an object-oriented database schema, constraint analysis makes use of semantics expressed as database constraints to support the flexible specification of propagation actions for operations on objects. Constraints are formally represented using Horn logic. The constraint analysis process then reasons about constraints at design time to help the designer understand the effects of constraints on object manipulation, identifying possible constraint violations as well as design alternatives for handling violations. An advantage of constraint analysis is that both inherent and explicit schema constraints are included in the analysis process. A formal representation is given that supports the analysis of constraints and the automatic identification of design alternatives for responding to constraint violations     

Reasoning about equations and functional dependencies on complexobjects

Virtually all semantic or object-oriented data models assume that objects have an identity separate from any of their parts, and allow users to define complex object types in which part values may be any other objects. This often results in a choice of query language in which a user can express navigating from one object to another by following a property value path. We consider a constraint language in which one may express equations and functional dependencies over complex object types. The language is novel in the sense that component attributes of individual constraints may correspond to property paths. The kind of equations we consider are also important, because they are a natural abstraction of the class of conjunctive queries for query languages that support property value navigation. In our introductory comments, we give an example of such a query and outline two applications of the constraint theory to problems relating to a choice of access plan for the query. We present a sound and complete axiomatization of the constraint language for the case in which interpretations are permitted to be infinite, where interpretations themselves correspond to a form of directed labeled graph. Although the implication problem for our form of equational constraint alone over arbitrary schema is undecidable, we present decision procedures for the implication problem for both kinds of constraints when the problem schema satisfies a stratification condition, and when all input functional dependencies are keys     

Constrained physical design tuning

Existing solutions to the automated physical design problem in database systems attempt to minimize execution costs of input workloads for a given storage constraint. In this work, we argue that this model is not flexible enough to address several real-world situations. To overcome this limitation, we introduce a constraint language that is simple yet powerful enough to express many important scenarios. We build upon a previously proposed transformation-based framework to incorporate constraints into the search space. We then show experimentally that we are able to handle a rich class of constraints and that our proposed technique scales gracefully. Our approach generalizes previous work that assumes simpler optimization models where configuration size is the only fixed constraint. As a consequence, the process of tuning a workload not only becomes more flexible, but also more complex, and getting the best design in the first attempt becomes difficult. We propose a paradigm shift for physical design tuning, in which sessions are highly interactive, allowing DBAs to quickly try different options, identify problems, and obtain physical designs in an agile manner.     

基于约束得分的动态集成选择算法

针对基于约束得分的特征选择容易受成对约束的组成和基数影响的问题, 提出了一种基于约束得分的动态集成选择算法（dynamic ensemble selection based on bagging constraint score, BCS-DES）。该算法将bagging约束得分（bagging constraint score, BCS）引入动态集成选择算法, 通过将样本空间划分为不同的区域, 使用多种群并行遗传算法为不同测试样本选择局部最优的分类集成, 达到提高分类精度的目的。在UCI实验数据集上进行的实验表明, BCS-DES算法较现有的特征选择算法受成对约束组成和基数影响更小, 效果更好。     

Constrained Portfolio Selection using Particle Swarm Optimization

This paper presents a novel heuristic method for solving an extended Markowitz mean–variance portfolio selection model. The extended model includes four sets of constraints: bounds on holdings, cardinality, minimum transaction lots and sector (or market/class) capitalization constraints. The first set of constraints guarantee that the amount invested (if any) in each asset is between its predetermined upper and lower bounds. The cardinality constraint ensures that the total number of assets selected in the portfolio is equal to a predefined number. The sector capitalization constraints reflect the investors’ tendency to invest in sectors with higher market capitalization value to reduce their risk of investment.The extended model is classified as a quadratic mixed-integer programming model necessitating the use of efficient heuristics to find the solution. In this paper, we propose a heuristic based on Particle Swarm Optimization (PSO) method. The proposed approach is compared with the Genetic Algorithm (GA). The computational results show that the proposed PSO effectively outperforms GA especially in large-scale problems.     

On the formulation and implementation of geometric and manufacturing constraints in node–based shape optimization

We introduce a novel method to handle geometrical and manufacturing constraints in parameter–free shape optimization. Therefore the design node coordinates are split in two sets where one set is declared as new design variables and the other set is coupled to the new design variables such that the geometrical constraint is fulfilled. Thereby no additional equations are appended to the optimization problem. In contrast the implementation of a demolding constraint is presented by formulating inequality constraints which indeed have to be attached to the optimization problem. In the context of a sensitivity–based shape optimization approach all manufacturing constraints have to be formulated in terms of the finite element node coordinates such that first order gradients with respect to the design node coordinates can be derived.     

MEER—An EER model enhanced with structure methods

Entity relationship (ER) schemas include cardinality constraints, that restrict the dependencies among entities within a relationship type. The cardinality constraints have direct impact on the application maintenance, since insertions or deletions of entities or relationships might affect related entities. Indeed, maintenance of a system or of a database can be strengthened to enforce consistency with respect to the cardinality constraints in a schema. Yet, once an ER schema is translated into a logical database schema, or translated within a system, the direct correlation between the cardinality constraints and maintenance transactions is lost, since the components of the ER schema might be decomposed among those of the logical database schema or the target system.In this paper, a full solution to the enforcement of cardinality constraints in EER schemas is given. We extend the enhanced ER (EER) data model with structure-based update methods that are fully defined by the cardinality constraints. The structure methods are provably terminating and cardinality faithful, i.e., they do not insert new inconsistencies and can only decrease existing ones. A refined approach towards measuring the cardinality consistency of a database is introduced. The contribution of this paper is in the automatic creation of update methods, and in building the formal basis for proving their correctness.     

Numerical constraints on XML data

Boundaries occur naturally in everyday life. This paper introduces numerical constraints into the framework of XML to take advantage of the benefits that result from the explicit specification of such boundaries. Roughly speaking, numerical constraints restrict the number of elements in an XML data fragment based on the data values of selected subelements. Efficient reasoning about numerical constraints provides effective means for predicting the number of answers to XQuery and XPath queries, the number of updates when using the XQuery update facility, and the number of encryptions or decryptions when using XML encryption. Moreover, numerical constraints can help to optimise XQuery and XPath queries, to exclude certain choices of indices from the index selection problem, and to generate views for efficient processing of common queries and updates.We investigate decision problems associated with numerical constraints in order to capitalise on the range of applications in XML data processing. To begin with we demonstrate that the implication problem is strongly coNP-hard for several classes of numerical constraints. These sources of potential intractability direct our attention towards the class of numerical keys that permit the specification of positive upper bounds. Numerical keys are of interest as they are reminiscent of cardinality constraints that are widely used in conceptual data modelling. At the same time, they form a natural generalisation of XML keys that are popular in XML theory and practice. We show that numerical keys are finitely satisfiable and establish a finite axiomatisation for their implication problem. Finally, we propose an algorithm that decides numerical key implication in quadratic time using shortest path methods.