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Categorical Foundations of Distributed Graph Transformation

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Graph Transformations (ICGT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4178))

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Abstract

A distributed graph (N,D) consists of a network graph N and a commutative diagram D over the scheme N which associates local graphs D(n i ) and graph morphisms D(e): D(n 1) →D(n 2) to nodes n 1, n 2 and edges e: n 1 →n 2 in N.

Although there are several interesting applications of distributed graphs and transformations, even the basic pushout constructions for the double pushout approach of distributed graph transformation could be shown up to now only in very special cases.

In this paper we show that the category of distributed graphs can be considered as a Grothendieck category over a specific indexed category, which assigns to each network N the category of all diagrams D of shape N. In this framework it is possible to give a free construction which allows to construct for each diagram D 1 over N 1 and network morphism h:N 1 →N 2 a free extension F h (D 1) over N 2 and to show that the Grothendieck category is complete and cocomplete if the underlying category of local graphs has these properties.

Moreover, an explicit construction for general pushouts of distributed graphs is given. This pushout construction is based on the free construction. The non-trivial proofs for free constructions and pushouts are the main contributions of this paper and they are compared with the special cases known up to now.

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Author information

Authors and Affiliations

  1. Technical University of Berlin, Germany

    Hartmut Ehrig & Ulrike Prange

  2. Technical University of Catalonia, Spain

    Fernando Orejas

Authors
  1. Hartmut Ehrig
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  2. Fernando Orejas
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  3. Ulrike Prange
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Editor information

Editors and Affiliations

  1. Institute of Business Communication and Information Science, University of Southern Denmark, 6000, Kolding, Denmark

    Andrea Corradini

  2. Technische Universität Berlin, Germany

    Hartmut Ehrig

  3. Dipartimento di Informatica, Università di Pisa,  

    Ugo Montanari

  4. Instituto de Informática, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

    Leila Ribeiro

  5. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

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© 2006 Springer-Verlag Berlin Heidelberg

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Ehrig, H., Orejas, F., Prange, U. (2006). Categorical Foundations of Distributed Graph Transformation. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds) Graph Transformations. ICGT 2006. Lecture Notes in Computer Science, vol 4178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841883_16

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  • DOI: https://doi.org/10.1007/11841883_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38870-8

  • Online ISBN: 978-3-540-38872-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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