The random_discrete_morse client in polymake is a C++ (and therefore FAST) implementation of Bruno Benedetti and Frank Lutz’s algorithm. Read more about it here.
The bistellar_simplification client in polymake uses a simulated annealing technique to determine the PL type of a simplicial complex. Read more about it here.
dgCat: Discrete Geometric Category
Let \(K\) be a simplicial complex and suppose that \(K\) collapses onto \(L\). Define \(n\) to be 1 less than the minimum number of collapsible sets it takes to cover \(L\). Then the discrete Lusternik-Schnirelmann category of \(K\) is the smallest \(n\) taken over all such \(L\). dgCat is an implementation of an algorithm which yields an upper bound for the discrete category. Read more about it here.
This project was joint work with Nicholas Scoville and Brian Green.