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An efficient decoding algorithm is a crucial element of any statistical machine translation system. Some researchers have noted certain similarities between SMT decoding and the famous Traveling Salesman Problem; in particular (Knight, 1999) has shown that any TSP instance can be mapped to a sub-case of a word-based SMT model, demonstrating NP-hardness of the decoding task. In this paper, we focus on the reverse mapping, showing that any phrase-based SMT decoding problem can be directly reformulated as a TSP. The transformation is very natural, deepens our understanding of the decoding problem, and allows direct use of any of the. | Phrase-Based Statistical Machine Translation as a Traveling Salesman Problem Mikhail Zaslavskiy Mines ParisTech Institut Curie 77305 Fontainebleau France mikhail.zaslavskiy@ensmp.fr Marc Dymetman Nicola Cancedda Xerox Research Centre Europe 38240 Meylan France marc.dymetman nicola.cancedda @xrce.xerox.com Abstract An efficient decoding algorithm is a crucial element of any statistical machine translation system. Some researchers have noted certain similarities between SMT decoding and the famous Traveling Salesman Problem in particular Knight 1999 has shown that any TSP instance can be mapped to a sub-case of a word-based SMT model demonstrating NP-hardness of the decoding task. In this paper we focus on the reverse mapping showing that any phrase-based SMT decoding problem can be directly reformulated as a TSP. The transformation is very natural deepens our understanding of the decoding problem and allows direct use of any of the powerful existing TSP solvers for SMT decoding. We test our approach on three datasets and compare a TSP-based decoder to the popular beam-search algorithm. In all cases our method provides competitive or better performance. 1 Introduction Phrase-based systems Koehn et al. 2003 are probably the most widespread class of Statistical Machine Translation systems and arguably one of the most successful. They use aligned sequences of words called biphrases as building blocks for translations and score alternative candidate translations for the same source sentence based on a log-linear model of the conditional probability of target sentences given the source sentence p T a S - exp V Xkhk S a T 1 Zs k where the hk are features that is functions of the source string S of the target string T and of the This work was conducted during an internship at XRCE. alignment a where the alignment is a representation of the sequence of biphrases that where used in order to build T from S The Xk s are weights and ZS is a normalization factor that guarantees .
