IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v156y2007i1p5-2410.1007-s10479-007-0231-z.html
   My bibliography  Save this article

Local search algorithms for finding the Hamiltonian completion number of line graphs

Author

Listed:
  • Paolo Detti
  • Carlo Meloni
  • Marco Pranzo

Abstract

Given a graph G=(V,E), the Hamiltonian completion number of G, HCN(G), is the minimum number of edges to be added to G to make it Hamiltonian. This problem is known to be $\mathcal{NP}$ -hard even when G is a line graph. In this paper, local search algorithms for finding HCN(G) when G is a line graph are proposed. The adopted approach is mainly based on finding a set of edge-disjoint trails that dominates all the edges of the root graph of G. Extensive computational experiments conducted on a wide set of instances allow to point out the behavior of the proposed algorithms with respect to both the quality of the solutions and the computation time. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Paolo Detti & Carlo Meloni & Marco Pranzo, 2007. "Local search algorithms for finding the Hamiltonian completion number of line graphs," Annals of Operations Research, Springer, vol. 156(1), pages 5-24, December.
    • Handle: RePEc:spr:annopr:v:156:y:2007:i:1:p:5-24:10.1007/s10479-007-0231-z
    DOI: 10.1007/s10479-007-0231-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-007-0231-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-007-0231-z?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. A. Agnetis & P. Detti & C. Meloni & D. Pacciarelli, 2001. "Set-Up Coordination between Two Stages of a Supply Chain," Annals of Operations Research, Springer, vol. 107(1), pages 15-32, October.
    2. Egon Balas & Alkis Vazacopoulos, 1998. "Guided Local Search with Shifting Bottleneck for Job Shop Scheduling," Management Science, INFORMS, vol. 44(2), pages 262-275, February.
    3. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liao, Ching-Jong & Shyu, Cian-Ci & Tseng, Chao-Tang, 2009. "A least flexibility first heuristic to coordinate setups in a two- or three-stage supply chain," International Journal of Production Economics, Elsevier, vol. 117(1), pages 127-135, January.
    2. Jorik Jooken & Pieter Leyman & Patrick Causmaecker, 2020. "A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs," Journal of Heuristics, Springer, vol. 26(5), pages 743-769, October.

    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. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    2. Helena Ramalhinho-Lourenço & Olivier C. Martin & Thomas Stützle, 2000. "Iterated local search," Economics Working Papers 513, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    4. Rossi, Andrea, 2014. "Flexible job shop scheduling with sequence-dependent setup and transportation times by ant colony with reinforced pheromone relationships," International Journal of Production Economics, Elsevier, vol. 153(C), pages 253-267.
    5. Fernandez del Pozo, J. A. & Bielza, C. & Gomez, M., 2005. "A list-based compact representation for large decision tables management," European Journal of Operational Research, Elsevier, vol. 160(3), pages 638-662, February.
    6. Jiafu Tang & Kai-Leung Yung & Iko Kaku & Jianbo Yang, 2008. "The scheduling of deliveries in a production-distribution system with multiple buyers," Annals of Operations Research, Springer, vol. 161(1), pages 5-23, July.
    7. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    8. Sels, Veronique & Craeymeersch, Kjeld & Vanhoucke, Mario, 2011. "A hybrid single and dual population search procedure for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 215(3), pages 512-523, December.
    9. Jun Pei & Xinbao Liu & Panos M. Pardalos & Wenjuan Fan & Shanlin Yang, 2017. "Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times," Annals of Operations Research, Springer, vol. 249(1), pages 175-195, February.
    10. J. Redondo & J. Fernández & I. García & P. Ortigosa, 2009. "A robust and efficient algorithm for planar competitive location problems," Annals of Operations Research, Springer, vol. 167(1), pages 87-105, March.
    11. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    12. Ali Shahabi & Sadigh Raissi & Kaveh Khalili-Damghani & Meysam Rafei, 2021. "Designing a resilient skip-stop schedule in rapid rail transit using a simulation-based optimization methodology," Operational Research, Springer, vol. 21(3), pages 1691-1721, September.
    13. Janssens, Jochen & Talarico, Luca & Sörensen, Kenneth, 2016. "A hybridised variable neighbourhood tabu search heuristic to increase security in a utility network," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 221-230.
    14. Wilson, Duncan T. & Hawe, Glenn I. & Coates, Graham & Crouch, Roger S., 2013. "A multi-objective combinatorial model of casualty processing in major incident response," European Journal of Operational Research, Elsevier, vol. 230(3), pages 643-655.
    15. Felipe, Ángel & Ortuño, M. Teresa & Righini, Giovanni & Tirado, Gregorio, 2014. "A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 111-128.
    16. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    17. Fathali, J. & Kakhki, H. Taghizadeh, 2006. "Solving the p-median problem with pos/neg weights by variable neighborhood search and some results for special cases," European Journal of Operational Research, Elsevier, vol. 170(2), pages 440-462, April.
    18. Wang, Wenyuan & Liu, Huakun & Tian, Qi & Xia, Zicheng & Liu, Suri & Peng, Yun, 2024. "An enhanced variable neighborhood search method for refrigerated container stacking and relocation problem with duplicate priorities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 188(C).
    19. Tengkuo Zhu & Stephen D. Boyles & Avinash Unnikrishnan, 2024. "Battery Electric Vehicle Traveling Salesman Problem with Drone," Networks and Spatial Economics, Springer, vol. 24(1), pages 49-97, March.
    20. Martín Barragán, Belén, 2016. "A Partial parametric path algorithm for multiclass classification," DES - Working Papers. Statistics and Econometrics. WS 22390, Universidad Carlos III de Madrid. Departamento de Estadística.

    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:annopr:v:156:y:2007:i:1:p:5-24:10.1007/s10479-007-0231-z. 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.