Morse theory is a fundamental tool for investigating the topology of smooth manifolds.
This tool has been extended to discrete structures by Forman, which allows combinatorial
analysis and direct computation. This theory relies on discrete gradient vector fields,
whose critical elements describe the topology of the structure. The purpose of this work
is to construct optimal discrete gradient vector fields, where optimality means having
the minimum number of critical elements. The problem is equivalently stated in terms of
maximal hyperforests of hypergraphs. Deduced from this theoretical result, a algorithm
constructing almost optimal discrete gradient fields is provided. The optimal parts of
the algorithm are proved, and the part of exponential complexity is replaced by
heuristics. Although reaching optimality is MAX-SNP hard, the experiments on odd
topological models are almost always optimal.