An incremental approach for maintaining functional dependencies

A vertex incremental approach for maintaining chordality

For a chordal graph G = (V, E), we study the problem of whether a new vertex u 6∈ V and a given set of edges between u and vertices in V can be added to G so that the resulting graph remains chordal. We show how to resolve this efficiently, and at the same time, if the answer is no, specify a maximal subset of the proposed edges that can be added along with u, or conversely, a minimal set of ex...

Incremental Discovery of Fuzzy Functional Dependencies

Mining Rare Association Rules by Discovering Quasi- Functional Dependencies: An Incremental Approach

Mining rare events is a critical task in several research areas such as database, machine learning, knowledge discovery, fraud detection, activity monitoring, and image analysis. In all these situations the main goal is to identify objects of a given population whose behavior is anomalous with respect to a set of rules part of the knowledge base, usually expressed by means of some statistical k...

An Axiomatic Approach to Defining Approximation Measures for Functional Dependencies

We consider the problem of defining an approximation measure for functional dependencies (FDs). An approximation measure for X → Y is a function mapping relation instances, r, to non-negative real numbers. The number to which r is mapped, intuitively, describes the “degree” to which the dependency X → Y holds in r. We develop a set of axioms for measures based on the following intuition. The de...

Convergence of an Approach for Solving Fredholm Functional Integral Equations

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.