There is a large number of different multiresolution approaches, each one with its preferred application. A more extensive summary can be found in [13].
The methods differ greatly in the time required for preprocessing. Multiresolution models are usually built iteratively by applying a sequence of simplification steps. Naturally, the more time is spent for generating the multiresolution representation, the better is the approximation of the original data at different resolutions. Selecting the optimal sequence for simplification can significantly reduce the number of triangles required to achieve a fixed approximation quality. Typically methods that take into account the original mesh at each simplification step produce better results at the cost of a more sophisticated (and time consuming) algorithm. This is necessary, if a global constraint is given by the user (although it is possible to take advantage of the locality of the individual steps, as used e.g. in [9,11]). This constraint can be expressed in different ways. Common choices include defining a geometrical error metric or using an energy function (as in [9]) to measure the accuracy of an approximation. On the other hand, using a local criterion for the guidance of the simplification process can be much faster. In this case, however, it is hard to assure a bounded precision, because locally estimated errors need to be accumulated in some way making an exact measurement impossible.
It is not always clear to which group a particular algorithm belongs. Some method of one class might be considered a special case of another class. The following list should be understood as a rough grouping of different methods according to their most important properties.