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IEEE/CAA Journal of Automatica Sinica

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Jie Chen, Kaiyi Luo, Changbing Tang, Zhao Zhang, and Xiang Li, "Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game," IEEE/CAA J. Autom. Sinica,doi: 10.1109/JAS.2022.105521
Citation: Jie Chen, Kaiyi Luo, Changbing Tang, Zhao Zhang, and Xiang Li, "Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game," IEEE/CAA J. Autom. Sinica,doi: 10.1109/JAS.2022.105521

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

doi: 10.1109/JAS.2022.105521
Funds:  This work was partly supported by the National Natural Science Foundation of China (61751303, U20A2068, 11771013), the Zhejiang Provincial Natural Science Foundation of China (LD19A010001), and the Fundamental Research Funds for the Central Universities
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  • Weighted vertex cover (WVC) is one of the most important combinatorial optimization problems. In this paper, we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks. We first model the WVC problem as a general game on weighted networks. Under the framework of a game, we newly define several cover states to describe the WVC problem. Moreover, we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums (SNEs) of the game. Then, we propose a game-based asynchronous algorithm (GAA), which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time. Subsequently, we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms, termed the improved game-based asynchronous algorithm (IGAA), in which we prove that it can obtain a better solution to the WVC problem than using a the GAA. Finally, numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.

     

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