IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v34y2022i2p817-833.html
   My bibliography  Save this article

A Fast Vertex Weighting-Based Local Search for Finding Minimum Connected Dominating Sets

Author

Listed:
  • Xinyun Wu

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, P.R. China)

  • Zhipeng Lü

    (SMART, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R. China)

  • Fred Glover

    (Department of Electrical, Computer and Energy Engineering, College of Engineering & Applied Science, University of Colorado Boulder, Boulder, Colorado 80309)

Abstract

The minimum connected dominating set (MCDS) problem consists of selecting a minimum set of vertices from an undirected graph, such that each vertex not in this set is adjacent to at least one of the vertices in it, and the subgraph induced by this vertex set is connected. This paper presents a fast vertex weighting (FVW) algorithm for solving the MCDS problem, which integrates several distinguishing features, such as a vertex weighting-based local search with tabu and perturbation strategies to help the search to jump out of the local optima, as well as a search space reduction strategy to improve the search efficiency. Computational experiments on four sets of 112 commonly used public benchmark instances, as well as 15 newly introduced sparse instances, show that FVW is highly competitive compared with the state-of-the-art algorithms in the literature despite its simplicity. FVW improves the previous best-known results for 20 large public benchmark instances while matching the best-known results for all but 2 of the remaining ones. Several ingredients of FVW are investigated to demonstrate the importance of the proposed ideas and techniques. Summary of Contribution: As a challenging classical NP-hard problem, the minimum connected dominating set (MCDS) problem has been studied for decades in the areas of both operations research and computer science, although there does not exist an exact polynomial algorithm for solving it. Thus, the new breakthrough on this classical NP-hard problem in terms of the computational results on classical benchmark instances is significant. This paper presents a new fast vertex weighting local search for solving the MCDS problem. Computational experiments on four sets of 112 commonly used public benchmark instances show that fast vertex weighting (FVW) is able to improve the previous best-known results for 20 large instances while matching the best-known results for all but 2 of the remaining instances. Several ingredients of FVW are also investigated to demonstrate the importance of the proposed ideas and techniques.

Suggested Citation

  • Xinyun Wu & Zhipeng Lü & Fred Glover, 2022. "A Fast Vertex Weighting-Based Local Search for Finding Minimum Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 817-833, March.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:2:p:817-833
    DOI: 10.1287/ijoc.2021.1106
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2021.1106
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2021.1106?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
    ---><---

    References listed on IDEAS

    as
    1. Abilio Lucena & Nelson Maculan & Luidi Simonetti, 2010. "Reformulations and solution algorithms for the maximum leaf spanning tree problem," Computational Management Science, Springer, vol. 7(3), pages 289-311, July.
    2. Edmund K. Burke & Yuri Bykov, 2016. "An Adaptive Flex-Deluge Approach to University Exam Timetabling," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 781-794, November.
    3. Anirudh Subramanyam & Panagiotis P. Repoussis & Chrysanthos E. Gounaris, 2020. "Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems Under Demand Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 661-681, July.
    4. Bernard Gendron & Abilio Lucena & Alexandre Salles da Cunha & Luidi Simonetti, 2014. "Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 645-657, November.
    5. Gao, Chao & Yao, Xin & Weise, Thomas & Li, Jinlong, 2015. "An efficient local search heuristic with row weighting for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 750-761.
    6. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
    7. Ruizhi Li & Shuli Hu & Huan Liu & Ruiting Li & Dantong Ouyang & Minghao Yin, 2019. "Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    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. Hamidreza Validi & Austin Buchanan, 2020. "The Optimal Design of Low-Latency Virtual Backbones," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 952-967, October.
    2. Yıldız, Barış & Karaşan, Oya Ekin, 2015. "Regenerator Location Problem and survivable extensions: A hub covering location perspective," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 32-55.
    3. Sourour Elloumi & Olivier Hudry & Estel Marie & Agathe Martin & Agnès Plateau & Stéphane Rovedakis, 2021. "Optimization of wireless sensor networks deployment with coverage and connectivity constraints," Annals of Operations Research, Springer, vol. 298(1), pages 183-206, March.
    4. Markus Leitner & Ivana Ljubić & Martin Riedler & Mario Ruthmair, 2019. "Exact Approaches for Network Design Problems with Relays," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 171-192, February.
    5. do Forte, Vinicius L. & Hanafi, Saïd & Lucena, Abilio, 2023. "Extended formulations for perfect domination problems and their algorithmic implications," European Journal of Operational Research, Elsevier, vol. 310(2), pages 566-581.
    6. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
    7. Li, Xiangyong & Aneja, Y.P., 2017. "Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms," European Journal of Operational Research, Elsevier, vol. 257(1), pages 25-40.
    8. Jiao Zhou & Zhao Zhang & Shaojie Tang & Xiaohui Huang & Ding-Zhu Du, 2018. "Breaking the O (ln n ) Barrier: An Enhanced Approximation Algorithm for Fault-Tolerant Minimum Weight Connected Dominating Set," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 225-235, May.
    9. Xiangyong Li & Y. P. Aneja, 2020. "A new branch-and-cut approach for the generalized regenerator location problem," Annals of Operations Research, Springer, vol. 295(1), pages 229-255, December.
    10. Mao Luo & Huigang Qin & Xinyun Wu & Caiquan Xiong, 2024. "A novel local search approach with connected dominating degree-based incremental neighborhood evaluation for the minimum 2-connected dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-26, July.
    11. Mats Carlsson & Sara Ceschia & Luca Gaspero & Rasmus Ørnstrup Mikkelsen & Andrea Schaerf & Thomas Jacob Riis Stidsen, 2023. "Exact and metaheuristic methods for a real-world examination timetabling problem," Journal of Scheduling, Springer, vol. 26(4), pages 353-367, August.
    12. Hosseinali Salemi & Austin Buchanan, 2022. "Solving the Distance-Based Critical Node Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1309-1326, May.
    13. Zhang, Yanzi & Diabat, Ali & Zhang, Zhi-Hai, 2021. "Reliable closed-loop supply chain design problem under facility-type-dependent probabilistic disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 180-209.
    14. Vic Grout, 2017. "A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application," Future Internet, MDPI, vol. 9(2), pages 1-11, May.
    15. Wang, Yiyuan & Pan, Shiwei & Al-Shihabi, Sameh & Zhou, Junping & Yang, Nan & Yin, Minghao, 2021. "An improved configuration checking-based algorithm for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 294(2), pages 476-491.
    16. Raka Jovanovic & Tatsushi Nishi & Stefan Voß, 2017. "A heuristic approach for dividing graphs into bi-connected components with a size constraint," Journal of Heuristics, Springer, vol. 23(2), pages 111-136, June.
    17. Si Chen & Ivana Ljubić & S. Raghavan, 2015. "The Generalized Regenerator Location Problem," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 204-220, May.
    18. Roshanaei, Vahid & Luong, Curtiss & Aleman, Dionne M. & Urbach, David R., 2020. "Reformulation, linearization, and decomposition techniques for balanced distributed operating room scheduling," Omega, Elsevier, vol. 93(C).
    19. Buchanan, Austin & Sung, Je Sang & Boginski, Vladimir & Butenko, Sergiy, 2014. "On connected dominating sets of restricted diameter," European Journal of Operational Research, Elsevier, vol. 236(2), pages 410-418.
    20. Ruizhi Li & Shuli Hu & Huan Liu & Ruiting Li & Dantong Ouyang & Minghao Yin, 2019. "Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.

    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:inm:orijoc:v:34:y:2022:i:2:p:817-833. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.