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International Conference on Graph Transformation

ICGT 2004: Graph Transformations pp 128–143Cite as

Towards Graph Programs for Graph Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3256))

Abstract

Graph programs as introduced by Habel and Plump [8] provide a simple yet computationally complete language for computing functions and relations on graphs. We extend this language such that numerical computations on labels can be conveniently expressed. Rather than resorting to some kind of attributed graph transformation, we introduce conditional rule schemata which are instantiated to (conditional) double-pushout rules over ordinary graphs. A guiding principle in our language extension is syntactic and semantic simplicity. As a case study for the use of extended graph programs, we present and analyse two versions of Dijkstra’s shortest path algorithm. The first program consists of just three rule schemata and is easily proved to be correct but can be exponential in the number of rule applications. The second program is a refinement of the first which is essentially deterministic and uses at most a quadratic number of rule applications.

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References

  1. Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. The MIT Press and McGraw-Hill (2000)

    Google Scholar 

  2. Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation — Part I: Basic concepts and double pushout approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1, ch. 3, pp. 163–245. World Scientific, Singapore (1997)

    Chapter  Google Scholar 

  3. Ehrig, H., Prange, U., Taentzer, G.: Fundamental theory for typed attributed graph transformation. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 161–177. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Ermel, C., Rudolf, M., Taentzer, G.: The AGG approach: Language and environment. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, ch. 14, pp. 551–603. World Scientific, Singapore (1999)

    Google Scholar 

  5. Habel, A., Heckel, R., Taentzer, G.: Graph grammars with negative application conditions. Fundamenta Informaticae 26(3/4), 287–313 (1996)

    MATH  MathSciNet  Google Scholar 

  6. Habel, A., Müller, J., Plump, D.: Double-pushout graph transformation revisited. Mathematical Structures in Computer Science 11(5), 637–688 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Habel, A., Plump, D.: A minimal and complete programming language for graph transformation (in preparation)

    Google Scholar 

  8. Habel, A., Plump, D.: Computational completeness of programming languages based on graph transformation. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 230–245. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Habel, A., Plump, D.: Relabelling in graph transformation. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 135–147. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Heckel, R., Küster, J., Taentzer, G.: Confluence of typed attributed graph transformation systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 161–176. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Jungnickel, D.: Graphs, Networks and Algorithms. Springer, Heidelberg (2002)

    Google Scholar 

  12. Kreowski, H.-J., Kuske, S.: Graph transformation units and modules. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, ch. 15, pp. 607–638. World Scientific, Singapore (1999)

    Google Scholar 

  13. Löwe, M., Korff, M., Wagner, A.: An algebraic framework for the transformation of attributed graphs. In: Sleep, R., Plasmeijer, R., van Eekelen, M. (eds.) Term Graph Rewriting: Theory and Practice, pp. 185–199. John Wiley, Chichester (1993)

    Google Scholar 

  14. Schied, G.: Uber Graphgrammatiken, eine Spezifikationsmethode für Programmiersprachen und Verteilte Regelsysteme. Doctoral dissertation, Universität Erlangen- Nürnberg, Volume 25(2) of Arbeitsberichte des Instituts für Informatik (1992) (in German)

    Google Scholar 

  15. Schürr, A., Winter, A., Zündorf, A.: The PROGRES approach: Language and environment. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, ch. 13, pp. 487–550. World Scientific, Singapore (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of York, York, YO10 5DD, UK

    Detlef Plump & Sandra Steinert

Authors
  1. Detlef Plump
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  2. Sandra Steinert
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Hartmut Ehrig

  2. University of Paderborn, Warburger Straße 100, 33098, Paderborn, Germany

    Gregor Engels

  3. George Mason University, Fairfax, Virginia, USA

    Francesco Parisi-Presicce

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

    Grzegorz Rozenberg

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© 2004 Springer-Verlag Berlin Heidelberg

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Plump, D., Steinert, S. (2004). Towards Graph Programs for Graph Algorithms. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds) Graph Transformations. ICGT 2004. Lecture Notes in Computer Science, vol 3256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30203-2_11

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  • DOI: https://doi.org/10.1007/978-3-540-30203-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23207-0

  • Online ISBN: 978-3-540-30203-2

  • eBook Packages: Springer Book Archive

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