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Social media9s explosive growth has resulted in a massive influx of electronic documents influencing various facets of daily life. However, the enormous and complex nature of this content makes extracting valuable insights challenging. Long document summarization emerges as a pivotal technique in this context, serving to distill extensive texts into concise and comprehensible summaries. This paper presents a novel three-stage pipeline for effective long document summarization. The proposed approach combines unsupervised and supervised learning techniques, efficiently handling large document sets while requiring minimal computational resources. Our methodology introduces a unique process for forming semantic chunks through spectral dynamic segmentation, effectively reducing redundancy and repetitiveness in the summarization process. Contrary to previous methods, our approach aligns each semantic chunk with the entire summary paragraph, allowing the abstractive summarization model to process documents without truncation and enabling the summarization model to deduce missing information from other chunks. To enhance the summary generation, we utilize a sophisticated rewrite model based on Bidirectional and Auto- Regressive Transformers (BART), rearranging and reformulating summary constructs to improve their fluidity and coherence. Empirical studies conducted on the long documents from the Webis-TLDR-17 dataset demonstrate that our approach significantly enhances the efficiency of abstractive summarization transformers. The contributions of this paper thus offer significant advancements in the field of long document summarization, providing a novel and effective methodology for summarizing extensive texts in the context of social media. 

In a sweep cover problem, mobile sensors move around to collect information from positions of interest (PoIs) periodically and timely. A PoI is sweep-covered if it is visited at least once in every time period t. In this paper, we study approximation algorithms on three types of sweep cover problems. The partial sweep cover problem (PSC) aims to use the minimum number of mobile sensors to sweep-cover at least a given number of PoIs. The prize-collecting sweep cover problem aims to minimize the cost of mobile sensors plus the penalties on those PoIs that are not sweep-covered. The budgeted sweep cover problem (BSC) aims to use a budgeted number N of mobile sensors to sweep-cover as many PoIs as possible. We propose a unified approach which can yield approximation algorithms for PSC and PCSC within approximation ratio at most 8, and a bicriteria (4, 1 2 )-approximation algorithm for BSC (that is, no more than 4N mobile sensors are used to sweep-cover at least 1 2 opt PoIs, where opt is the number of PoIs that can be sweep-covered by an optimal solution). Furthermore, our results for PSC and BSC can be extended to their weighted version, and our algorithm for PCSC answers a question proposed in Liang etal. (Theor Comput Sci, 2022) on PCSC