We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, And-Or graphs, relational data bases and transportation analysis are presented. January 1990 Revised, October 1992 ( * ) This research has been supported in part by the "Comitato Nazionale Scienza e Tecnologia dell'Informazione", National Research Council of Italy, under Grant n.89.00208.12, and in part by research grants from the National Research Council of Canada. 1 Dipartimento di Informatica, Università di Pisa, Italy 2 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada 2 INTRODUCTION Hypergraphs, a generaliz...

The advent of graphical workstations lead to a new generation of interaction tools in database systems, where the use of graphics greatly enhances the quality of the interaction. Yet, Visual Query Languages (VQLs) present some limitations, deriving partly from their own paradigm and partly from the available technology. One of the basic drawbacks is the lack of formalization, in contrast to the wellestablished traditional languages. In this paper we propose a theoretical framework for visual interaction with databases, having a particular kind of hypergraph, the Structure Modeling Hypergraph (SMH), as a representation tool, able to capture the features of existing data models. SMHs profit from the basic property of diagrams while overcoming their limitations. Notable characteristics of SMHs are: uniform and unified representation of intensional and extensional aspects of databases, direct representation of containment relationships, and immediate applicability of direct manipulation p...