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Calculating Graph Algorithms for Dominance and Shortest Path

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Mathematics of Program Construction (MPC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7342))

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Abstract

We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length.

The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation.

This work was carried out while the first author was visiting Aarhus University in the fall of 2011.

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Author information

Authors and Affiliations

  1. KU Leuven, Belgium

    Ilya Sergey & Dave Clarke

  2. Aarhus University, Denmark

    Jan Midtgaard

Authors
  1. Ilya Sergey
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  2. Jan Midtgaard
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  3. Dave Clarke
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Jeremy Gibbons

  2. Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, 28660, Boadilla del Monte, Madrid, Spain

    Pablo Nogueira

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Sergey, I., Midtgaard, J., Clarke, D. (2012). Calculating Graph Algorithms for Dominance and Shortest Path. In: Gibbons, J., Nogueira, P. (eds) Mathematics of Program Construction. MPC 2012. Lecture Notes in Computer Science, vol 7342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31113-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-31113-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31112-3

  • Online ISBN: 978-3-642-31113-0

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