@MISC{Denero_thecomplexity, author = {John Denero and Dan Klein}, title = {The Complexity of Phrase Alignment Problems}, year = {} }
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Abstract
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. 1