scholarly journals Belief Propagation for Maximum Coverage on Weighted Bipartite Graph and Application to Text Summarization

2020 ◽  
Vol 89 (4) ◽  
pp. 043801
Author(s):  
Hiroki Kitano ◽  
Koujin Takeda
Author(s):  
Marina Litvak ◽  
Natalia Vanetik

The problem of extractive summarization for a collection of documents is defined as the problem of selecting a small subset of sentences so that the contents and meaning of the original document set are preserved in the extract in best possible way. In this chapter, the authors present a linear model for the problem of extractive text summarization, where they strive to obtain a summary that preserves the information coverage as much as possible in comparison to the original document set. The authors measure the information coverage in terms and reduce the summarization task to the maximum coverage problem. They construct a system of linear inequalities that describes the given document set and its possible summaries and translate the problem of finding the best summary to the problem of finding the point on a convex polytope closest to the given hyperplane. This re-formulated problem can be solved efficiently with the help of linear programming. The experimental results show the partial superiority of our introduced approach over other systems participated in the generic multi-document summarization tasks of the DUC 2002 and the MultiLing 2013 competitions.


2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Huibin Feng ◽  
Zhaocai Yu ◽  
Jian Guan ◽  
Geng Lin

Energy Internet (EI) is aimed at sustainable computing by integrating various energy forms into a highly flexible grid similar to the Internet. The network subsystems of EI connect different components to enable real-time monitoring, controlling, and management. In this paper, the spectrum allocation problem of the cognitive radio network for EI in a smart city is investigated. The network spectrum allocation with both heterogeneous primary operators and secondary users is formulated as the combinatorial auction problem and then is converted to a subset selection problem on a weighted bipartite graph. We propose a hybrid algorithm to solve the problem. Firstly, the proposed algorithm uses a constructive procedure based on the Kuhn-Munkres algorithm to obtain an initial solution. Then, a local search is used to improve the solution quality. In addition, the truthfulness of the auction is guaranteed by adopting a “Vickrey-like” mechanism. Simulation results show that the performance of the proposed algorithm is better than existing greedy algorithms in terms of the social welfare, seller revenue, buyer satisfaction ratio, and winning buyer ratio.


2011 ◽  
Vol 38 (12) ◽  
pp. 14514-14522 ◽  
Author(s):  
Rasim M. Alguliev ◽  
Ramiz M. Aliguliyev ◽  
Makrufa S. Hajirahimova ◽  
Chingiz A. Mehdiyev

2017 ◽  
Vol 31 (7) ◽  
pp. e3471 ◽  
Author(s):  
Jiangtao Ma ◽  
Yaqiong Qiao ◽  
Guangwu Hu ◽  
Tong Li ◽  
Yongzhong Huang ◽  
...  

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