###### Abstract  
Large Language Models (LLMs) have shown a strong performance across various tasks but still face challenges in automatic text summarization. While they are effective in capturing semantic patterns from large corpora, they typically lack mechanisms for encoding structural relationships between sentences or paragraphs. Their high hardware requirements and limited analysis as to processing efficiency further constrain their applicability. This paper proposes a framework employing the Graph Independent Set approach to extract the essence of textual graphs and address the limitations of LLMs. The framework encapsulates nodes and relations into structural graphs generated through Natural Language Processing (NLP) techniques based on the Maximum Independent Set (MIS) theory. The incorporation of graph-derived structural features enables more semantically cohesive and accurate summarization outcomes. Experiments on the Document Understanding Conference (DUC) and Cable News Network (CNN)/DailyMail datasets are conducted with different summary lengths to evaluate the performance of the framework. The proposed method provides up to a 41.05% (Recall-Oriented Understudy for Gisting Evaluation, ROUGE-2 F1) increase in summary quality and a 60.71% improvement in response times on models such as XLNet, Pegasus, and DistilBERT. The proposed framework enables more informative and concise summaries by embedding structural relationships into LLM-driven semantic representations, while reducing computational costs. In this study, we explore whether integrating MIS-based graph filtering with LLMs significantly enhances both the accuracy and efficiency of extractive text summarization.  
graph theory; maximum independent set; LLM; NLP; text summarization +
Footnote †: 2020: _Article_  
necessity of integrating structural information into LLMs to improve their summarization performance and produce more contextually coherent summaries.  
This paper proposes a novel framework based on the MIS theory to address several limitations of LLMs. These include hardware-related issues such as high computational costs, a limited capacity to process lengthy documents, and significant energy consumption. The framework also targets content-related challenges, including repetitive outputs, the omission of key information, and the lack of structural awareness due to a dependence on training strategies. By modeling textual data as simplified, independent graphs, the proposed method extracts structural features using the MIS algorithm as its core component. Integrating these features with semantic content allows the generation of more coherent and informative summaries. The framework also facilitates a better representation of cause-effect relationships, contributing to an improved summary quality and reliability of output.  
The framework begins with preprocessing to prepare documents for structural analysis. It then constructs graph representations that capture relationships between sentences based on shared phrases and semantic similarity. Using the MIS algorithm, the framework identifies independent structures within these graphs to reduce redundancy and simplify the input. This allows LLMs to work with a more structured and concise dataset, improving both the summarization speed and efficiency. Rather than processing entire documents, the model focuses on key sentence connections, which enhances energy efficiency and reduces computational demands. By incorporating structural information, the framework also helps to optimize the input data and mitigates misleading guidance during inference. Experiments conducted on the CNN/DailyMail and DUC-2002 datasets demonstrate that the framework consistently produces accurate and coherent summaries. The approach improves summarization performance by reducing redundancy, minimizing information loss, and lowering the reliance on specific training data and strategies.