We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homol-ogy computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that… (More)
Two implementations of a homology algorithm based on the Forman's discrete Morse theory combined with the coreduction method are presented. Their efficiency is compared with other implementations of homology algorithms.
We present an efficient algorithm for constructing piecewise constant Lyapunov functions for dynamics generated by a continuous nonlinear map defined on a compact metric space. We provide a memory efficient data structure for storing nonuniform grids on which the Lyapunov function is defined and give bounds on the complexity of the algorithm for both time… (More)