## Abstract

Decoding of phrase-based translation models in the general case is known to be NP complete, by a reduction from the traveling salesman problem (Knight, 1999). In practice, phrase-based systems often impose a hard distortion limit that limits the movement of phrases during translation. However, the impact on complexity after imposing such a constraint is not well studied. In this paper, we describe a dynamic programming algorithm for phrase-based decoding with a fixed distortion limit. The runtime of the algorithm is O(n d! l h^{d+1}) where n is the sentence length, d is the distortion limit, l is a bound on the number of phrases starting at any position in the sentence, and h is related to the maximum number of target language translations for any source word. The algorithm makes use of a novel representation that gives a new perspective on decoding of phrase-based models.