Abstract
After two decades of 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 behavior 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 constructing mathematical counter-examples. This paper is therefore a first attempt at reporting, classifying and analyzing test cases previously used for algorithmic work in Reeb analysis (contour trees and Reeb graphs), and the expression of a philosophy of how to test topological code.
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Acknowledgements
In the UK, this work was supported by the Engineering and Physical Sciences Research Council (EPSRC) project EP/J013072/1. In the US, this work was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration and by the Director, Office of Science, Office of Advanced Scientific Computing Research, of the U.S. Department of Energy under Contract No. DE- 392 AC02-05CH11231. In France, this work was supported by the BPI grant “AVIDO” (Programme 393 d’Investissements d’Avenir, reference P112017-2661376/DOS0021427).
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Carr, H., Tierny, J., Weber, G.H. (2020). Pathological and Test Cases for Reeb Analysis. 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. https://doi.org/10.1007/978-3-030-43036-8_7
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