Carr, H orcid.org/0000-0001-6739-0283, Tierny, J and Weber, GH (2020) Pathological and Test Cases For Reeb Analysis. In: Topological Methods in Data Analysis and Visualization V. Mathematics and Visualization book series . Springer , pp. 103-120. ISBN 978-3-030-43035-1
Abstract
After two decades in computational topology, it is clearly a computationally challenging area. Not only do we have the usual algorithmic and programming difficulties with establishing correctness, we also have a class of problems that are mathematically complex and notationally fragile. Effective development and deployment therefore requires an additional step - construction or selection of suitable test cases. Since we cannot test all possible inputs, our selection of test cases expresses our understanding of the task and of the problems involved. Moreover, the scale of the data sets we work with is such that, no matter how unlikely the behaviour mathematically, it is nearly guaranteed to occur at scale in every run. The test cases we choose are therefore tightly coupled with mathematically pathological cases, and need to be developed using the skills expressed most obviously in the constructing mathematical counterexamples. This paper is therefore a first attempt at reporting, classifying and analysing test cases previously used in computational topology, and the expression of a philosophy of how to test topological code.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2020. This is an author accepted version of a chapter published in Carr H., Fujishiro I., Sadlo F., Takahashi S. (eds) Topological Methods in Data Analysis and Visualization V. TopoInVis 2017. Mathematics and Visualization. Springer, Cham. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Computational Topology, Reeb Space, Reeb Graph, Contour Tree, Reeb Analysis |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/J013072/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Apr 2019 15:00 |
Last Modified: | 11 Dec 2022 01:13 |
Status: | Published |
Publisher: | Springer |
Series Name: | Mathematics and Visualization book series |
Identification Number: | 10.1007/978-3-030-43036-8_7 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144396 |