Question: How does the model compare with the MMR baseline?
Evidence: Various classes of NP-hard problems involving a submodular and non-decreasing function can be solved approximately by polynomial time algorithms with provable approximation factors. Algorithms "Detection of hypergraph transversals for text summarization" and "Detection of hypergraph transversals for text summarization" are our core methods for the detection of approximations of maximal budgeted hypergraph transversals and minimal soft hypergraph transversals, respectively. In each case, a transversal is found and the summary is formed by extracting and aggregating the associated sentences. Algorithm "Detection of hypergraph transversals for text summarization" is based on an adaptation of an algorithm presented in BIBREF30 for the maximization of submodular functions under a Knaspack constraint. It is our primary transversal-based summarization model, and we refer to it as the method of Transversal Summarization with Target Length (TL-TranSum algorithm). Algorithm "Detection of hypergraph transversals for text summarization" is an application of the algorithm presented in BIBREF20 for solving the submodular set covering problem. We refer to it as Transversal Summarization with Target Coverage (TC-TranSum algorithm). Both algorithms produce transversals by iteratively appending the node inducing the largest increase in the total weight of the covered hyperedges relative to the node weight. While long sentences are expected to cover more themes and induce a larger increase in the total weight of covered hyperedges, the division by the node weights (i.e. the sentence lengths) balances this tendency and allows the inclusion of short sentences as well. In contrast, the methods of sentence selection based on a maximal relevance and a minimal redundancy such as, for instance, the maximal marginal relevance approach of BIBREF31 , tend to favor the selection of long sentences only. The main difference between algorithms "Detection of hypergraph transversals for text summarization" and "Detection of hypergraph transversals for text summarization" is the stopping criterion: in algorithm "Detection of hypergraph transversals for text summarization" , the approximate minimal soft transversal is obtained whenever the targeted hyperedge coverage is reached while algorithm "Detection of hypergraph transversals for text summarization" appends a given sentence to the approximate maximal budgeted transversal only if its addition does not make the summary length exceed the target length $L$ .
FLOAT SELECTED: Table 2: Comparison with related graph- and hypergraph-based summarization systems.
While long sentences are expected to cover more themes and induce a larger increase in the total weight of covered hyperedges, the division by the node weights (i.e. the sentence lengths) balances this tendency and allows the inclusion of short sentences as well. In contrast, the methods of sentence selection based on a maximal relevance and a minimal redundancy such as, for instance, the maximal marginal relevance approach of BIBREF31 , tend to favor the selection of long sentences only.
FLOAT SELECTED: Table 2: Comparison with related graph- and hypergraph-based summarization systems.
Answer: The answers are shown as follows:
*  Moreover, our TL-TranSum method also outperforms other approaches such as MaxCover ( $5\%$ ) and MRMR ( $7\%$ )