In this paper we build upon results of Padua and Wolfe, who introduced two graph transformations to break dependence paths including anti- and output-dependences. We first formalize these two transformations. Then, given a loop nest, we aim at determining which statements should be transformed so as to break artificial dependence paths involving anti- or output-dependences. The problem of finding the minimum number of statements to be transformed is shown to be NP-complete, and we propose two efficient heuristics.