However, as phrase-based decoding casts translation as a string concatenation problem and permits arbitrary permutations, it proves to be NP-complete (Knight, 1999).
phrase reordering modeling has attracted intensive attention in the past decade (e.g., Tillman, 2004;Zens et al., 2004;Al-Onaizan and Papineni, 2006;Xiong et al., 2006;Koehn et al., 2007;Galley and Manning, 2008;Feng et al., 2010;Green et al., 2010;Bisazza and Federico, 2012;Cherry, 2013).