Recent studies on extractive text summarization formulate it as a combinatorial optimization problem such as a Knapsack Problem , a Maximum Coverage Problem or a Budgeted Median Problem . These methods successfully improved summarization quality , but they did not consider the rhetorical relations between the textual units of a source document . Thus , summaries generated by these methods may lack logical coherence . This paper proposes a single document summarization method based on the trimming of a discourse tree . This is a two-fold process . First , we propose rules for transforming a rhetorical structure theorybased discourse tree into a dependency-based discourse tree , which allows us to take a treetrimming approach to summarization . Second , we formulate the problem of trimming a dependency-based discourse tree as a Tree Knapsack Problem , then solve it with integer linear programming ( ILP ) . Evaluation results showed that our method improved ROUGE scores . State-of-the-art extractive text summarization methods regard a document ( or a document set ) as a set of textual units ( e.g. sentences , clauses , phrases ) and formulate summarization as a combinatorial optimization problem , i.e. selecting a subset of the set of textual units that maximizes an objective without violating a length constraint . For example , Mc-Donald ( 2007 ) formulated text summarization as a Knapsack Problem , where he selects a set of textual units that maximize the sum of significance scores of each unit . Filatova et al . ( 2004 ) proposed a summarization method based on a Maximum Coverage Problem , in which they select a set of textual units that maximizes the weighted sum of the conceptual units ( e.g. unigrams ) contained in the set . Although , their greedy solution is only an approximation , Takamura et al . ( 2009a ) extended it to obtain the exact solution . More recently , Takamura et al . ( 2009b ) regarded summarization as a Budgeted Median Problem and obtain exact solutions with integer linear programming . These methods successfully improved ROUGE ( Lin , 2004 ) scores , but they still have one critical shortcoming . Since these methods are based on subset selection , the summaries they generate can not preserve the rhetorical structure of the textual units of a source document . Thus , the resulting summary may lack coherence and may not include significant textual units from a source document . One powerful and potential way to overcome the problem is to include discourse tree constraints in the summarization procedure . Marcu ( 1998 ) regarded a document as a Rhetorical Structure Theory ( RST ) ( William Charles , Mann and Sandra Annear , Thompson , 1988 ) -based discourse tree ( RST-DT ) and selected textual units according to a preference ranking derived from the tree structure to make a summary . Daumé et al . ( 2002 ) proposed a document compression method that directly models the probability of a summary given an RST-DT by using a noisy-channel model . These methods generate well-organized summaries , however , since they do not formulate summarizations as combinatorial op-Figure 1 : Example RST-DT from ( Marcu , 1998 ) . timization problems , the optimality of the generated summaries is not guaranteed . In this paper , we propose a single document summarization method based on the trimming of a discourse tree based on the Tree Knapsack Problem . If a discourse tree explicitly represents parent-child relationships between textual units , we can apply the well-known tree-trimming approach to a discourse tree and reap the benefit of combinatorial optimization methods . In other words , to apply the treetrimming approach , we need a tree whose all nodes represent textual units . Unfortunately , the RST-DT does not allow it , because textual units in the RST-DT are located only on leaf nodes and parent-child relationship between textual units are represented implicitly at higher positions in a tree . Therefore , we first propose rules that transform an RST-DT into a dependency-based discourse tree ( DEP-DT ) that explicitly defines the parent-child relationships . Second , we treat it as a rooted subtree selection , in other words , a Tree Knapsack Problem and formulate the problem as an ILP . 2 From RST-DT to DEP-DT This paper proposed rules for transforming an RST-DT to a DEP-DT to obtain the parent-child relationships between EDUs . We treated a single document summarization method as a Tree Knapsack Problem , i.e. the summarizer selects the best rooted subtree from a DEP-DT . To demonstrate the effectiveness of our method , we conducted an experimental evaluation using 30 documents selected from the RST Discourse Treebank Corpus . The results showed that our method achieved the highest ROUGE-1,2 scores .

Challenge: Existing optimization-based methods for extractive summarization do not consider the rhetorical relations between textual units leading to generating uncoherent summaries or missing significant textual units.
Approach: They propose to first transform a rhetorical discourse tree into a dependency-based tree and then trim it as a Tree Knapsack Problem.
Outcome: The proposed method achieves the highest ROUGE-1,2 scores on 30 documents selected from the RST Discourse Treebank Corpus.