An algorithm for calculating top-dimensional bounding chains
- Published
- Accepted
- Subject Areas
- Algorithms and Analysis of Algorithms, Data Science, Scientific Computing and Simulation
- Keywords
- Homology, Computational Algebraic Topology
- Copyright
- © 2017 Carvalho et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2017. An algorithm for calculating top-dimensional bounding chains. PeerJ Preprints 5:e3151v1 https://doi.org/10.7287/peerj.preprints.3151v1
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.
Author Comment
This is a submission to PeerJ Computer Science for review.
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