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.