IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v458y2023ics0096300323004332.html
   My bibliography  Save this article

Graphical representation and hierarchical decomposition mechanism for vertex-cover solution space

Author

Listed:
  • Wei, Wei
  • Feng, Xiangnan

Abstract

NP problems act essential roles in modelling and analysing various complex systems, and representation learning of system individuals and relations has faced the kernel difficulty in understanding the complexity and solving the NP problems. In this paper, solution space organisation of minimum vertex-cover problem is deeply investigated using the famous König-Egérvary (KE) graph and theorem, in which a hierarchical decomposition mechanism named KE-layer structure of general graphs is proposed to reveal the complexity of vertex-cover. To achieve the graphical representation and hierarchical decomposition, an algorithm to verify the KE graph is given by the solution space expression of vertex-cover, and the relation between multi-layer KE graphs and maximal matching is illustrated and proved. Furthermore, a framework to calculate the KE-layer number and approximate the minimal vertex-cover is provided, with different strategies of switching nodes and counting energy. The phase transition phenomenon between different KE-layers is studied with the transition points located, and searching of vertex-cover got by this strategy presents comparable advantage against several other methods. Its efficiency outperforms the existing ones just before the transition point. The graphical representation and hierarchical decomposition provide a new perspective to illustrate the structural organisations of graphs better, and its formation mechanism can help reveal the intrinsic complexity and establish heuristic strategy for large-scale graphs/systems recognition.

Suggested Citation

  • Wei, Wei & Feng, Xiangnan, 2023. "Graphical representation and hierarchical decomposition mechanism for vertex-cover solution space," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004332
    DOI: 10.1016/j.amc.2023.128264
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323004332
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128264?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. W. Kuhn, 1956. "Variants of the hungarian method for assignment problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(4), pages 253-258, December.
    2. David Silver & Julian Schrittwieser & Karen Simonyan & Ioannis Antonoglou & Aja Huang & Arthur Guez & Thomas Hubert & Lucas Baker & Matthew Lai & Adrian Bolton & Yutian Chen & Timothy Lillicrap & Fan , 2017. "Mastering the game of Go without human knowledge," Nature, Nature, vol. 550(7676), pages 354-359, October.
    3. Laura Alessandretti & Piotr Sapiezynski & Vedran Sekara & Sune Lehmann & Andrea Baronchelli, 2018. "Evidence for a conserved quantity in human mobility," Nature Human Behaviour, Nature, vol. 2(7), pages 485-491, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daníelsson, Jón & Macrae, Robert & Uthemann, Andreas, 2022. "Artificial intelligence and systemic risk," Journal of Banking & Finance, Elsevier, vol. 140(C).
    2. Adnan Jafar & Alessandra Kobayati & Michael A. Tsoukas & Ahmad Haidar, 2024. "Personalized insulin dosing using reinforcement learning for high-fat meals and aerobic exercises in type 1 diabetes: a proof-of-concept trial," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    3. Yang, Zhengzhi & Zheng, Lei & Perc, Matjaž & Li, Yumeng, 2024. "Interaction state Q-learning promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    4. Zhang, Yihao & Chai, Zhaojie & Lykotrafitis, George, 2021. "Deep reinforcement learning with a particle dynamics environment applied to emergency evacuation of a room with obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    5. Keller, Alexander & Dahm, Ken, 2019. "Integral equations and machine learning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 2-12.
    6. Canhoto, Ana Isabel & Clear, Fintan, 2020. "Artificial intelligence and machine learning as business tools: A framework for diagnosing value destruction potential," Business Horizons, Elsevier, vol. 63(2), pages 183-193.
    7. Zhaobin Mo & Xuan Di & Rongye Shi, 2023. "Robust Data Sampling in Machine Learning: A Game-Theoretic Framework for Training and Validation Data Selection," Games, MDPI, vol. 14(1), pages 1-13, January.
    8. Yang, Kaiyuan & Huang, Houjing & Vandans, Olafs & Murali, Adithya & Tian, Fujia & Yap, Roland H.C. & Dai, Liang, 2023. "Applying deep reinforcement learning to the HP model for protein structure prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    9. Yifeng Guo & Xingyu Fu & Yuyan Shi & Mingwen Liu, 2018. "Robust Log-Optimal Strategy with Reinforcement Learning," Papers 1805.00205, arXiv.org.
    10. Xueqing Yan & Yongming Li, 2023. "A Novel Discrete Differential Evolution with Varying Variables for the Deficiency Number of Mahjong Hand," Mathematics, MDPI, vol. 11(9), pages 1-21, May.
    11. José A. Torres-León & Marco A. Moreno-Armendáriz & Hiram Calvo, 2024. "Representing the Information of Multiplayer Online Battle Arena (MOBA) Video Games Using Convolutional Accordion Auto-Encoder (A 2 E) Enhanced by Attention Mechanisms," Mathematics, MDPI, vol. 12(17), pages 1-19, September.
    12. Jianjun Chen & Weihao Hu & Di Cao & Bin Zhang & Qi Huang & Zhe Chen & Frede Blaabjerg, 2019. "An Imbalance Fault Detection Algorithm for Variable-Speed Wind Turbines: A Deep Learning Approach," Energies, MDPI, vol. 12(14), pages 1-15, July.
    13. Andrew G. Haldane & Arthur E. Turrell, 2019. "Drawing on different disciplines: macroeconomic agent-based models," Journal of Evolutionary Economics, Springer, vol. 29(1), pages 39-66, March.
    14. Antonopoulos, Ioannis & Robu, Valentin & Couraud, Benoit & Kirli, Desen & Norbu, Sonam & Kiprakis, Aristides & Flynn, David & Elizondo-Gonzalez, Sergio & Wattam, Steve, 2020. "Artificial intelligence and machine learning approaches to energy demand-side response: A systematic review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 130(C).
    15. Lu Wang & Wenqing Ai & Tianhu Deng & Zuo‐Jun M. Shen & Changjing Hong, 2020. "Optimal production ramp‐up in the smartphone manufacturing industry," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(8), pages 685-704, December.
    16. Karwowski, Jan & Mańdziuk, Jacek, 2019. "A Monte Carlo Tree Search approach to finding efficient patrolling schemes on graphs," European Journal of Operational Research, Elsevier, vol. 277(1), pages 255-268.
    17. Young Joon Park & Yoon Sang Cho & Seoung Bum Kim, 2019. "Multi-agent reinforcement learning with approximate model learning for competitive games," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-20, September.
    18. Hai Wang & Shengnan Chen, 2023. "Insights into the Application of Machine Learning in Reservoir Engineering: Current Developments and Future Trends," Energies, MDPI, vol. 16(3), pages 1-11, January.
    19. Morato, P.G. & Andriotis, C.P. & Papakonstantinou, K.G. & Rigo, P., 2023. "Inference and dynamic decision-making for deteriorating systems with probabilistic dependencies through Bayesian networks and deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    20. Yanning Ge & Tao Huang & Xiaoding Wang & Guolong Zheng & Xu Yang, 2024. "The Application of Residual Connection-Based State Normalization Method in GAIL," Mathematics, MDPI, vol. 12(2), pages 1-14, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004332. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.