An algorithm for calculating top-dimensional bounding chains
We describe the 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 esti...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
PeerJ Inc.
2018-05-01
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| Series: | PeerJ Computer Science |
| Subjects: | |
| Online Access: | https://peerj.com/articles/cs-153.pdf |
| Summary: | We describe the 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. |
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| ISSN: | 2376-5992 |