An algorithm for calculating top-dimensional bounding chains

Abstract

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.

Keywords

• Homology
• Computational algebraic topology