IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v42y2021i2d10.1007_s10878-020-00652-7.html
   My bibliography  Save this article

Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search

Author

Listed:
  • Andrei Nikolaev

    (P. G. Demidov Yaroslavl State University)

  • Anna Kozlova

    (P. G. Demidov Yaroslavl State University)

Abstract

We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. A sufficient condition for vertex adjacency in the 1-skeleton of the traveling salesperson polytope can be formulated as the Hamiltonian decomposition problem in a 4-regular multigraph. We introduce a heuristic general variable neighborhood search algorithm for this problem based on finding a vertex-disjoint cycle cover of the multigraph through reduction to perfect matching and several cycle merging operations. The algorithm has a one-sided error: the answer “not adjacent” is always correct, and was tested on random directed and undirected Hamiltonian cycles and on pyramidal tours.

Suggested Citation

  • Andrei Nikolaev & Anna Kozlova, 2021. "Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search," Journal of Combinatorial Optimization, Springer, vol. 42(2), pages 212-230, August.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:2:d:10.1007_s10878-020-00652-7
    DOI: 10.1007/s10878-020-00652-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00652-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-020-00652-7?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Pierre Hansen & Nenad Mladenović & Raca Todosijević & Saïd Hanafi, 2017. "Variable neighborhood search: basics and variants," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 423-454, September.
    2. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    3. M. L. Balinski, 1985. "Signature Methods for the Assignment Problem," Operations Research, INFORMS, vol. 33(3), pages 527-536, June.
    4. Marko Mladenović & Thierry Delot & Gilbert Laporte & Christophe Wilbaut, 2020. "The parking allocation problem for connected vehicles," Journal of Heuristics, Springer, vol. 26(3), pages 377-399, June.
    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. Andrei V. Nikolaev & Egor V. Klimov, 2024. "Finding a second Hamiltonian decomposition of a 4-regular multigraph by integer linear programming," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-31, July.
    2. Uttam Bandyopadhyay & Atanu Biswas & Shirsendu Mukherjee, 2009. "Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 13-33, March.
    3. Pritibhushan Sinha, 2009. "Assignment problems with changeover cost," Annals of Operations Research, Springer, vol. 172(1), pages 447-457, November.
    4. Preety Srivastava & Xueyan Zhao, 2010. "What Do the Bingers Drink? Micro‐Unit Evidence on Negative Externalities and Drinker Characteristics of Alcohol Consumption by Beverage Types," Economic Papers, The Economic Society of Australia, vol. 29(2), pages 229-250, June.
    5. Holger Schwender & Margaret A. Taub & Terri H. Beaty & Mary L. Marazita & Ingo Ruczinski, 2012. "Rapid Testing of SNPs and Gene–Environment Interactions in Case–Parent Trio Data Based on Exact Analytic Parameter Estimation," Biometrics, The International Biometric Society, vol. 68(3), pages 766-773, September.
    6. Chen, Liang & Tokuda, Naoyuki, 2001. "A faster data assignment algorithm for maximum likelihood-based multitarget motion tracking with bearings-only measurements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 109-120.
    7. Matysková, Ludmila & Rogers, Brian & Steiner, Jakub & Sun, Keh-Kuan, 2020. "Habits as adaptations: An experimental study," Games and Economic Behavior, Elsevier, vol. 122(C), pages 391-406.
    8. André, Kévin, 2013. "Applying the Capability Approach to the French Education System: An Assessment of the "Pourquoi pas moi ?"," ESSEC Working Papers WP1316, ESSEC Research Center, ESSEC Business School.
    9. Weikang Fang & Zailin Guan & Peiyue Su & Dan Luo & Linshan Ding & Lei Yue, 2022. "Multi-Objective Material Logistics Planning with Discrete Split Deliveries Using a Hybrid NSGA-II Algorithm," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    10. Irina Zrnić Novaković & Dean Ajduković & Helena Bakić & Camila Borges & Margarida Figueiredo-Braga & Annett Lotzin & Xenia Anastassiou-Hadjicharalambous & Chrysanthi Lioupi & Jana Darejan Javakhishvil, 2023. "Shaped by the COVID-19 pandemic: Psychological responses from a subjective perspective–A longitudinal mixed-methods study across five European countries," PLOS ONE, Public Library of Science, vol. 18(4), pages 1-32, April.
    11. Ruiz-Frau, A. & Krause, T. & Marbà, N., 2018. "The use of sociocultural valuation in sustainable environmental management," Ecosystem Services, Elsevier, vol. 29(PA), pages 158-167.
    12. Yexin Tian & Shuo Xu & Yuchen Cao & Zhongyan Wang & Zijing Wei, 2025. "An Empirical Comparison of Machine Learning and Deep Learning Models for Automated Fake News Detection," Mathematics, MDPI, vol. 13(13), pages 1-24, June.
    13. AlMalki, Hameeda A. & Durugbo, Christopher M., 2023. "Evaluating critical institutional factors of Industry 4.0 for education reform," Technological Forecasting and Social Change, Elsevier, vol. 188(C).
    14. Eduardo G. Pardo & Antonio García-Sánchez & Marc Sevaux & Abraham Duarte, 2020. "Basic variable neighborhood search for the minimum sitting arrangement problem," Journal of Heuristics, Springer, vol. 26(2), pages 249-268, April.
    15. Guevara, C. Angelo & Fukushi, Mitsuyoshi, 2016. "Modeling the decoy effect with context-RUM Models: Diagrammatic analysis and empirical evidence from route choice SP and mode choice RP case studies," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 318-337.
    16. Melo, Grace & Palma, Marco A. & Ribera, Luis A., 2024. "Are experts overoptimistic about the success of food market labeling information?," 2024 Annual Meeting, July 28-30, New Orleans, LA 343870, Agricultural and Applied Economics Association.
    17. Abraham Duarte & Eduardo G. Pardo, 2020. "Special issue on recent innovations in variable neighborhood search," Journal of Heuristics, Springer, vol. 26(3), pages 335-338, June.
    18. Qin, Xiaolin & Tang, Juan & Feng, Yong & Bachmann, Bernhard & Fritzson, Peter, 2016. "Efficient index reduction algorithm for large scale systems of differential algebraic equations," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 10-22.
    19. Alexandra I. Khalyasmaa & Pavel V. Matrenin & Stanislav A. Eroshenko & Vadim Z. Manusov & Andrey M. Bramm & Alexey M. Romanov, 2022. "Data Mining Applied to Decision Support Systems for Power Transformers’ Health Diagnostics," Mathematics, MDPI, vol. 10(14), pages 1-25, July.
    20. Arnaldo Rabello de Aguiar Vallim Filho & Daniel Farina Moraes & Marco Vinicius Bhering de Aguiar Vallim & Leilton Santos da Silva & Leandro Augusto da Silva, 2022. "A Machine Learning Modeling Framework for Predictive Maintenance Based on Equipment Load Cycle: An Application in a Real World Case," Energies, MDPI, vol. 15(10), pages 1-41, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:jcomop:v:42:y:2021:i:2:d:10.1007_s10878-020-00652-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.