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Computational Topology via Functional Programming: A Baseline Analysis

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Topological Methods in Data Analysis and Visualization III

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Computational topology is of interest in visualization because it summarizes useful global properties of a dataset. The greatest need for such abstractions is in massive data, and to date most implementations have opted for low-level languages to obtain space and time-efficient implementations. Such code is complex, and is becoming even more so with the need to operate efficiently on a range of parallel hardware. Motivated by rapid advances in functional programming and compiler technology, this chapter investigates whether a shift in programming paradigm could reduce the complexity of the task. Focusing on contour tree generation as a case study, the chapter makes three contributions. First, it sets out the development of a concise functional implementation of the algorithm. Second, it shows that the sequential functional code can be tuned to match the performance of an imperative implementation, albeit at some cost in code clarity. Third, it outlines new possiblilities for parallelisation using functional tools, and notes similarities between functional abstractions and emerging ideas in extreme-scale visualization.

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Notes

  1. 1.

    This is a simplification. Technically, lazy evaluation is the combination of normal order reduction with overwriting the root of reducible expressions to ensure that arguments are evaluated at most once.

  2. 2.

    www.volvis.org

  3. 3.

    Timings were performed on an Apple MacBook, measured using the unix ‘time’ command. Programs were compiled with -O2 -prof -rtsopts -auto-all -rtsopts, enabling optimization and run-time profiling.

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Acknowledgements

Support for this work was provided by the UK Engineering and Physical Sciences Research Council under Grant EP/J013072/1.

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Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, UK

    David Duke & Hamish Carr

Authors
  1. David Duke
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  2. Hamish Carr
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Corresponding author

Correspondence to David Duke .

Editor information

Editors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, USA

    Peer-Timo Bremer

  2. Comparative Visualization Group, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, Germany

    Ingrid Hotz

  3. School of Computing and SCI Institute, University of Utah, Salt Lake City, Utah, USA

    Valerio Pascucci

  4. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Ronald Peikert

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Duke, D., Carr, H. (2014). Computational Topology via Functional Programming: A Baseline Analysis. In: Bremer, PT., Hotz, I., Pascucci, V., Peikert, R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-04099-8_5

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