Alignment and distribution is NOT (always) NP-hard

In this paper, an efficient algorithm to simultaneously implement array alignment and data/computation distribution is introduced and evaluated. We re-visit previous work of Li and Chen [13, 14], and we show that their alignment step should not be conducted without preserving the potential parallelism. In other words, the optimal alignment may well sequentialize computations, whatever the distribution afterwards. We provide an efficient algorithm that handles alignment and data/computation distribution simultaneously. The good news is that several important instances of the whole alignment/distribution problem have polynomial complexity, while alignment itself is NP-complete [13]. Keywords: compilation techniques, parallel loops, alignment, distribution, "the owner computes" rule. R'esum'e Dans ce rapport, un algorithme efficace est pr'esent'e et 'evalu'e pour r'esoudre simultan'ement l'alignement des tableaux et la distribution des donn'ees et des calculs. Nous revisitons les travau..