Efficient summarization with polytopes

The problem of extractive summarization for a collection of documents is defined as the problem of selecting a small subset of sentences so that the contents and meaning of the original document set are preserved in the extract in best possible way. In this chapter, the authors present a linear model for the problem of extractive text summarization, where they strive to obtain a summary that preserves the information coverage as much as possible in comparison to the original document set. The authors measure the information coverage in terms and reduce the summarization task to the maximum coverage problem. They construct a system of linear inequalities that describes the given document set and its possible summaries and translate the problem of finding the best summary to the problem of finding the point on a convex polytope closest to the given hyperplane. This re-formulated problem can be solved efficiently with the help of linear programming. The experimental results show the partial superiority of our introduced approach over other systems participated in the generic multi-document summarization tasks of the DUC 2002 and the MultiLing 2013 competitions.