Polynomial Time Joint Structural Inference for Sentence Compression

We propose two polynomial time inference algorithms to compress sentences under bigram and dependency-factored objectives. The first algorithm is exact and requires O(n6) running time. It extends Eisner’s cubic time parsing algorithm by using virtual dependency arcs to link deleted words. Two signatures are added to each span, indicating the number of deleted words and the rightmost kept word within the span. The second algorithm is a fast approximation of the first one. It relaxes the compression ratio constraint using Lagrangian relaxation, and thereby requires O(n4) running time. Experimental results on the popular sentence compression corpus demonstrate the effectiveness and efficiency of our proposed approach.