Variability models play a key role in software product line engineering as they are used to represent the common and variable features that products may include, and what constraints among the features must be satisfied to guarantee the validity of the products. Valuable analysis operations on variability models can be performed by black box reusing logic engines, such as SAT-solvers and binary decision diagram libraries. Unfortunately, such kind of reuse implies long computation times for operations that need calling the engines many times. To overcome this problem, we propose new algorithms that directly deal with the data structure of a binary decision diagram encoding a variability model. In particular, our algorithms are specifically designed to detect core & dead features, and the impact & exclusion sets of every feature.