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Transition Refinement for Deriving a Distributed Minimum Weight Spanning Tree Algorithm

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Application and Theory of Petri Nets 2002 (ICATPN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2360))

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Abstract

The algorithm of Gallager, Humblet, and Spira computes the minimum spanning tree of a weighted graph in a distributed fashion. Though based on a simple mathematical idea, this algorithm is hard to understand because of the complex communication between the distributed agents.

There are several attempts to prove the correctness of this algorithm but most of the proofs are either incomplete or extremely long and technical and, therefore, difficult to comprehend.

This paper reports on a new model and a new correctness proof for the algorithm. Model and proof are given in a sequence of 12 property preserving refinement steps, starting with a simple non-distributed algorithm. All algorithms are modelled by Algebraic Petri nets. We justify 8 of the refinement steps using well-known refinement methods for distributed algorithms. The other four steps can not be justified using traditional refinement methods. Their correctness is proved by using the new concept of transition refinement which we introduced in [16].

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Author information

Authors and Affiliations

  1. Software Verification Research Centre, The University of Queensland, Brisbane, Australia

    Sibylle Peuker

Authors
  1. Sibylle Peuker
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Editor information

Editors and Affiliations

  1. Division of Informatics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings Mayfield Road, Edinburgh, EH9 3JZ, UK

    Javier Esparza

  2. Department of Computer Science, University of Adelaide, North Terrace, Adelaide, SA, 5005, Australia

    Charles Lakos

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© 2002 Springer-Verlag Berlin Heidelberg

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Peuker, S. (2002). Transition Refinement for Deriving a Distributed Minimum Weight Spanning Tree Algorithm. In: Esparza, J., Lakos, C. (eds) Application and Theory of Petri Nets 2002. ICATPN 2002. Lecture Notes in Computer Science, vol 2360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48068-4_22

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  • DOI: https://doi.org/10.1007/3-540-48068-4_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43787-1

  • Online ISBN: 978-3-540-48068-6

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