Directed Hypergraphs—Models, Algorithms, Applications

Dear Colleagues,

Directed hypergraphs are generalizations of directed graphs. They can model rules and provide straightforward and intuitive interpretations in several contexts where graphs cannot capture essential properties.

Unlike graphs, where basic notions—such as path, reachability, size of a path, etc.—are shared among scholars, the analogous notions for hypergraphs have various versions and interpretations, leading to different models with dramatically different properties. Additionally, the corresponding decision and optimization problems can be described by radically diverse computational complexities.

However, despite their branched nature, a number of domains have adopted directed hypergraphs as perfect tools to represent problem instances and provide computational support for tackling problems of paramount importance.

As an example, in chemistry and biomedicine, the notion of pathways within networks of molecules, metabolites, proteins or genes provides intuitive representations of possible sequences of transformations or interactions, each involving several entities (not just two, as would be possible to capture by using graphs) that can occur in a given context.

Several authoritative texts have been written on directed hypergraphs. However, the evolution of theory and models, aside from the growing number of applications, has created a scenario where it is not easy, even for researchers, to choose a coherent set of ingredients with which to find a suitable solution for the situation under consideration. In some contexts, the scholars are tempted to reinvent the wheel as this may seem easier than selecting the algorithms that can provably work in their specific setting.

These situations bring to the main motivations of this Special Issue, which is intended to provide an assessment of reference material concerning directed hypergraphs, including known notions, new techniques, and relevant examples of the application of this ubiquitous model to some domain.

Contributions containing either new results or surveys will be considered for this Special Issue. Submitted work may seek to assess:

1. the notion(s) of directed hypergraphs, including a characterization of complexity for decision and optimization problems, as well as suitable algorithms;
2. some of the domains in which directed hypergraphs have been successfully applied in order to provide a transparent interpretation of the notions of a hyperpath, as well as the measures and consequent optimality of a hyperpath; this should be accompanied by addressing the best available solutions for the raised problems.

In either case, we invite the authors to make available, where possible, the source code of the presented techniques.

Prof. Umberto Nanni
Dr. Paolo Fantozzi
Guest Editors

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• directed hypergraph
• directed hyperpath
• shortest hyperpath
• hyperpath optimization
• pathway
• pathway analysis