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A Functional, Successor List Based Version of Warshall’s Algorithm with Applications

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Relational and Algebraic Methods in Computer Science (RAMICS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6663))

Abstract

We show how formally and systematically to develop a purely functional version of Warshall’s algorithm for computing transitive closures by combining the unfold-fold technique, relation-algebra and data refinement. It is based on an implementation of relations by lists of successor lists. The final version can immediately be implemented in Haskell. This resulting Haskell program has the same runtime complexity as the traditional imperative array-based implementation of Warshall’s algorithm. We also demonstrate how it can be re-used as component in other functional algorithms.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität Kiel, Olshausenstraße 40, D-24098, Kiel, Germany

    Rudolf Berghammer

Authors
  1. Rudolf Berghammer
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

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Berghammer, R. (2011). A Functional, Successor List Based Version of Warshall’s Algorithm with Applications. In: de Swart, H. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2011. Lecture Notes in Computer Science, vol 6663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21070-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-21070-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21069-3

  • Online ISBN: 978-3-642-21070-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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