Many phrase alignment models operate over the combinatorial space of bijective phrase alignments. We prove that finding an optimal alignment in this space is NP-hard, while computing alignment expectations is #P-hard. On the other hand, we show that the problem of finding an optimal alignment can be cast as an integer linear program, which provides a simple, declarative approach to Viterbi inference for phrase alignment models that is empirically quite efficient.
REF consider the phrase alignment problem, that is, the problem of finding an optimal phrase-based alignment for a sourcelanguage/target-language sentence pair.
The Complexity of Phrase Alignment Problems
Annual Meeting Of The Association For Computational Linguistics
Computer Science