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Directed hypergraphs as a modelling paradigm

Gli ipergrafi orientati come strumento per la modellazione e la soluzione di problemi decisionali

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Abstract

We address a generalization of graphs, the directed hypergraphs, and show that they are a powerful tool in modelling and solving several relevant problems in many application areas. Such application areas include Linear Production Problems, Flexible Manufacturing Systems, Propositional Logic, Relational Databases, and Public Transportation Systems.

Riassunto

Gli ipergrafi orientati costitniscono uno strumento di notevole efficacia nella modellazione e soluzione di diverse classi di problemi decisionali. Essi costituiscono un linguaggio unificante per problemi che nascono in ambienti molto diversi, quali “Sistemi di Produzione”, “Sistemi di Trasporto Pubblico”, “Basi di Dati Relazionali” …

Particolarmente importanti sono i concetti di ipercammino e di iperflusso che generlizzano in modo naturale quelli di cammino e di flusso su grafi orientati. fpercammini e iperflussi ottimi possono essere trovati per mezzo di algoritmi specializzati, che generalizzano gli algoritmi di etichettatura per la ricerca di cammini minimi e quelli di tipo “simplesso su reti” per i flussi di costo minimo.

Ci si propone di presentare alcuni dei contesti più rilevanti, dal punto di vista delle applicazioni pratiche, in cui possono essere utilizzati modelli e algoritmi basati su ipergrafi orientati. Particolare attenzione sarà rivolta alle applicazioni di tipo economico aziendale.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia, 40, 56125, Pisa

    Giorgio Gallo & Maria Grazia Scutellà

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  1. Giorgio Gallo
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  2. Maria Grazia Scutellà
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Correspondence to Giorgio Gallo.

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Gallo, G., Scutellà, M.G. Directed hypergraphs as a modelling paradigm. Decisions Econ Finan 21, 97–123 (1998). https://doi.org/10.1007/BF02735318

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