An algorithm for calculating top-dimensional bounding chains
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Abstract
We describe the \textsc{Coefficient-Flow} algorithm for calculating the bounding chain of an $(n-1)$--boundary on an $n$--manifold-like simplicial complex $S$. We prove its correctness and show that it has a computational time complexity of $O(|S^{(n-1)}|)$ (where $S^{(n-1)}$ is the set of $(n-1)$--faces of $S$). We estimate the big-$O$ coefficient which depends on the dimension of $S$ and the implementation. We present an implementation, experimentally evaluate the complexity of our algorithm, and compare its performance with that of solving the underlying linear system.
Cite this as
2017. An algorithm for calculating top-dimensional bounding chains. PeerJ Preprints 5:e3151v1 https://doi.org/10.7287/peerj.preprints.3151v1note This preprint is not peer-reviewed. You may wish to reference the subsequent peer-reviewed version of this article.
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This is a submission to PeerJ Computer Science for review.
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Supplemental Information
data used to produce the (timing) results presented in the text
Files with data used to produce Table 1 and the graphs in Figure 2. All timings were obtained by running the tests available in the code repository https://www.github.com/crvs/coeff-flow
Additional Information
Competing Interests
The authors declare that they have no competing interests.
Author Contributions
J. Frederico Carvalho conceived and designed the experiments, performed the experiments, analyzed the data, wrote the paper, prepared figures and/or tables, performed the computation work, reviewed drafts of the paper.
Mikael Vejdemo-Johansson reviewed drafts of the paper.
Danica Kragic reviewed drafts of the paper.
Florian T. Pokorny reviewed drafts of the paper.
Data Deposition
The following information was supplied regarding data availability:
repository: github
url: www.github.com/crvs/coeff-flow
Funding
This work has been supported by the Knut and Alice Wallenberg Foundation and the Swedish Research Council. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
