Tree trimming is the problem of extracting an optimal subtree from an input tree, and sentence extraction and sentence compression methods can be formulated and solved as tree trimming problems. Previous approaches require integer linear programming (ILP) solvers to obtain exact solutions. The problem of this approach is that ILP solvers are black-boxes and have no theoretical guarantee as to their computation complexity. We propose a dynamic programming (DP) algorithm for tree trimming problems whose running time is O(NLlogN), where N is the number of tree nodes andL is the length limit. Our algorithm exploits the zero-suppressed binary decision diagram (ZDD), a data structure that represents a family of sets as a directed acyclic graph, to represent the set of subtrees in a compact form; the structure of ZDD permits the application of DP to obtain exact solutions, and our algorithm is applicable to different tree trimming problems. Moreover, experiments show that our algorithm is faster than state-of-the-art ILP solvers, and that it scales well to handle large summarization problems.
['Masaaki Nishino', 'Norihito Yasuda', 'Tsutomu Hirao', 'Shin-ichi Minato', 'Masaaki Nagata']
A Dynamic Programming Algorithm for Tree Trimming-based Text Summarization