Study, representation and applications of hypergraph minimal transversals

TL;DR

This paper explores new applications and optimization methods for hypergraph minimal transversals, including social network analysis, reducing transversal sets, and hypergraph decomposition, supported by experimental validation.

Contribution

It introduces three novel methods for applying and optimizing hypergraph minimal transversals, including social network detection, irredundant representation, and hypergraph decomposition.

Findings

Effective detection of important social network actors.

Reduction of minimal transversal sets via irredundant hypergraphs.

Successful hypergraph decomposition and transversal generation.

Abstract

This work is part of the field of the hypergraph theory and focuses on hypergraph minimal transversal. The problem of extracting the minimal transversals from a hypergraph received the interest of many researchers as shown the number of algorithms proposed in the literature, and this is mainly due to the solutions offered by the minimal transversal in various application areas such as databases, artificial intelligence, e-commerce, semantic web, etc. In view of the wide range of fields of minimal transversal application and the interest they generate, the objective of this thesis is to explore new application paths of minimal transversal by proposing methods to optimize the extraction. This has led to three proposed contributions in this thesis. The first approach takes advantage of the emergence of Web 2.0 and, therefore, social networks using minimal transversal for the detection of important actors within these networks. The second part of research in this thesis has focused on reducing the number of hypergraph minimal transversal. A concise and accurate representation of minimal transversal was proposed and is based on the construction of an irredundant hypergraph, hence are calculated the irredundant minimal transversal of the initial hypergraph. An application of this representation to the dependency inference problem is presented to illustrate the usefulness of this approach. The last approach includes the hypergraph decomposition into partial hypergraph the local minimal transversal are calculated and their Cartesian product can generate all the hypergraph transversal sets. Different experimental studies have shown the value of these proposed approaches.