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.
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