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Simple Rectangle-Based Functional Programs for Computing Reflexive-Transitive Closures

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Relational and Algebraic Methods in Computer Science (RAMICS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7560))

Abstract

We show how to systematically derive simple purely functional algorithms for computing the reflexive-transitive closure of directed graphs. Directed graphs can be represented as binary relations and we develop our algorithms based on a relation-algebraic description of reflexive-transitive closures. This description employs the relation-algebraic notion of rectangles and instantiating the resulting algorithm with different kinds of rectangles leads to different algorithms for computing reflexive-transitive closures. Using data refinement, we then develop simple Haskell programs for two specific choices of rectangles and show that one of them has cubic runtime like an imperative implementation of Warshall’s standard algorithm.

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Author information

Authors and Affiliations

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

    Rudolf Berghammer & Sebastian Fischer

Authors
  1. Rudolf Berghammer
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  2. Sebastian Fischer
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Editors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  2. Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, CB3 0FD, Cambridge, UK

    Timothy G. Griffin

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Berghammer, R., Fischer, S. (2012). Simple Rectangle-Based Functional Programs for Computing Reflexive-Transitive Closures. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-33314-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33313-2

  • Online ISBN: 978-3-642-33314-9

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