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Efficient and Effective Directed Minimum Spanning Tree Queries

Author

Listed:
  • Zhuoran Wang

    (Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou 511400, China
    These authors contributed equally to this work.)

  • Dian Ouyang

    (Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou 511400, China
    These authors contributed equally to this work.)

  • Yikun Wang

    (Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou 511400, China)

  • Qi Liang

    (Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou 511400, China)

  • Zhuo Huang

    (Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou 511400, China)

Abstract

Computing directed Minimum Spanning Tree ( D M S T ) is a fundamental problem in graph theory. It is applied in a wide spectrum of fields from computer network and communication protocol design to revenue maximization in social networks and syntactic parsing in Natural Language Processing. State-of-the-art solutions are online algorithms that compute D M S T for a given graph and a root. For multi-query requirements, the online algorithm is inefficient. To overcome the drawbacks, in this paper, we propose an indexed approach that reuses the computation result to facilitate single and batch queries. We store all the potential edges of D M S T in a hierarchical tree in O ( n ) space complexity. Furthermore, we answer the D M S T query of any root in O ( n ) time complexity. Experimental results demonstrate that our approach can achieve a speedup of 2–3 orders of magnitude in query processing compared to the state-of-the-art while consuming O(n) index size.

Suggested Citation

  • Zhuoran Wang & Dian Ouyang & Yikun Wang & Qi Liang & Zhuo Huang, 2023. "Efficient and Effective Directed Minimum Spanning Tree Queries," Mathematics, MDPI, vol. 11(9), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2200-:d:1141029
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    References listed on IDEAS

    as
    1. Peng Yue & Qing Cai & Wanfeng Yan & Wei-Xing Zhou, 2020. "Information flow networks of Chinese stock market sectors," Papers 2004.08759, arXiv.org.
    2. Gao, Leitao & Zhao, Guangshe & Li, Guoqi & Liu, Yuming & Huang, Jiangshuai & Deng, Lei, 2019. "Containment control of directed networks with time-varying nonlinear multi-agents using minimum number of leaders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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