Approximation Strategies for Multi-Structure Sentence Compression

Sentence compression has been shown to benefit from joint inference involving both n-gram and dependency-factored objectives but this typically requires expensive integer programming. We explore instead the use of Lagrangian relaxation to decouple the two subproblems and solve them separately. While dynamic programming is viable for bigram-based sentence compression, finding optimal compressed trees within graphs is NP-hard. We recover approximate solutions to this problem using LP relaxation and maximum spanning tree algorithms, yielding techniques that can be combined with the efficient bigrambased inference approach using Lagrange multipliers. Experiments show that these approximation strategies produce results comparable to a state-of-the-art integer linear programming formulation for the same joint inference task along with a significant improvement in runtime.