IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n156901.html

The Capacity Expansion Path Problem in Networks

Author

Listed:
  • Jianping Li
  • Juanping Zhu

Abstract

This paper considers the general capacity expansion path problem (GCEP) for the telecommunication operators. We investigate the polynomial equivalence between the GCEP problem and the constrained shortest path problem (CSP) and present a pseudopolynomial algorithm for the GCEP problem, no matter the graph is acyclic or not. Furthermore, we investigate two special versions of the GCEP problem. For the minimum number arc capacity expansion path problem (MN‐CEP), we give a strongly polynomial algorithm based on the dynamic programming. For the minimum‐cost capacity expansion shortest path problem (MCESP), we give a strongly polynomial algorithm by constructing a shortest paths network.

Suggested Citation

  • Jianping Li & Juanping Zhu, 2013. "The Capacity Expansion Path Problem in Networks," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:156901
    DOI: 10.1155/2013/156901
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/156901
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/156901?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. Onur Şeref & Ravindra K. Ahuja & James B. Orlin, 2009. "Incremental Network Optimization: Theory and Algorithms," Operations Research, INFORMS, vol. 57(3), pages 586-594, June.
    2. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
    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. Bowen Cui & Jianwei Zhang, 2025. "Exact and Approximation Algorithms for Task Offloading with Service Caching and Dependency in Mobile Edge Computing," Future Internet, MDPI, vol. 17(6), pages 1-20, June.
    2. Esaignani Selvarajah & Rui Zhang, 2014. "Supply chain scheduling to minimize holding costs with outsourcing," Annals of Operations Research, Springer, vol. 217(1), pages 479-490, June.
    3. Randeep Bhatia & Sudipto Guha & Samir Khuller & Yoram J. Sussmann, 1998. "Facility Location with Dynamic Distance Functions," Journal of Combinatorial Optimization, Springer, vol. 2(3), pages 199-217, September.
    4. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.
    5. Boaz Golany & Moshe Kress & Michal Penn & Uriel G. Rothblum, 2012. "Network Optimization Models for Resource Allocation in Developing Military Countermeasures," Operations Research, INFORMS, vol. 60(1), pages 48-63, February.
    6. Hradovich, Mikita & Kasperski, Adam & Zieliński, Paweł, 2019. "Robust recoverable 0–1 optimization problems under polyhedral uncertainty," European Journal of Operational Research, Elsevier, vol. 278(1), pages 136-148.
    7. Xie, Chi & Travis Waller, S., 2012. "Parametric search and problem decomposition for approximating Pareto-optimal paths," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1043-1067.
    8. Fragkos, Ioannis & Cordeau, Jean-François & Jans, Raf, 2021. "Decomposition methods for large-scale network expansion problems," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 60-80.
    9. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh, 2011. "Dynamic Programming-Based Column Generation on Time-Expanded Networks: Application to the Dial-a-Flight Problem," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 105-119, February.
    10. Anita Schöbel & Reena Urban, 2022. "The Cheapest Ticket Problem in Public Transport," Transportation Science, INFORMS, vol. 56(6), pages 1432-1451, November.
    11. Buu-Chau Truong & Kim-Hung Pho & Van-Buol Nguyen & Bui Anh Tuan & Wing-Keung Wong, 2019. "Graph Theory And Environmental Algorithmic Solutions To Assign Vehicles Application To Garbage Collection In Vietnam," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(3), pages 1-35, September.
    12. Michael Holzhauser & Sven O. Krumke, 2018. "A generalized approximation framework for fractional network flow and packing problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 19-50, February.
    13. Junyan Su & Qiulin Lin & Minghua Chen, 2025. "Optimizing carbon footprint in long-haul heavy-duty E-Truck transportation," Nature Communications, Nature, vol. 16(1), pages 1-16, December.
    14. Luigi Di Puglia Pugliese & Francesca Guerriero, 2013. "A Reference Point Approach for the Resource Constrained Shortest Path Problems," Transportation Science, INFORMS, vol. 47(2), pages 247-265, May.
    15. Chen, Xujin & Hu, Jie & Hu, Xiaodong, 2009. "A polynomial solvable minimum risk spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 198(1), pages 43-46, October.
    16. Jenkins , Alan, 2005. "Performance Appraisal Research: A Critical Review of Work on “The Social Context and Politics of Appraisal”," ESSEC Working Papers DR 05004, ESSEC Research Center, ESSEC Business School.
    17. Junran Lichen & Jianping Li & Ko-Wei Lih & Xingxing Yu, 0. "Approximation algorithms for constructing required subgraphs using stock pieces of fixed length," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-22.
    18. Vittorio Bilò & Ioannis Caragiannis & Angelo Fanelli & Michele Flammini & Gianpiero Monaco, 2017. "Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems," Post-Print hal-02089412, HAL.
    19. Jianping Li & Weidong Li & Junran Lichen, 2014. "The subdivision-constrained routing requests problem," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 152-163, January.
    20. Mattia, Sara & Rossi, Fabrizio & Servilio, Mara & Smriglio, Stefano, 2017. "Staffing and scheduling flexible call centers by two-stage robust optimization," Omega, Elsevier, vol. 72(C), pages 25-37.

    More about this item

    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:wly:jnljam:v:2013:y:2013:i:1:n:156901. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.