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This paper describes a new method to compare reordering constraints for Statistical Machine Translation. We investigate the best possible (oracle) Bleu score achievable under different reordering constraints. Using dynamic programming, we efficiently find a reordering that approximates the highest attainable Bleu score given a reference and a set of reordering constraints. We present an empirical evaluation of popular reordering constraints: local constraints, the IBM constraints, and the Inversion Transduction Grammar (ITG) constraints. We present results for a German-English translation task and show that reordering under the ITG constraints can improve over the baseline by more than 7.5 Bleu points.

Comparing reordering constraints for SMT using efficient Bleu oracle computation