IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n743908.html

On the 2‐MRS Problem in a Tree with Unreliable Edges

Author

Listed:
  • Wei Ding
  • Yu Zhou
  • Guangting Chen
  • Hongfa Wang
  • Guangming Wang

Abstract

This paper extends the well‐known most reliable source (1‐MRS) problem in unreliable graphs to the 2‐most reliable source (2‐MRS) problem. Two kinds of reachable probability models of node pair in unreliable graphs are considered, that is, the superior probability and united probability. The 2‐MRS problem aims to find a node pair in the graph from which the expected number of reachable nodes or the minimum reachability is maximized. It has many important applications in large‐scale unreliable computer or communication networks. The #P‐hardness of the 2‐MRS problem in general graphs follows directly from that of the 1‐MRS problem. This paper deals with four models of the 2‐MRS problem in unreliable trees where every edge has an independent working probability and devises a cubic‐time and quadratic‐space dynamic programming algorithm, respectively, for each model.

Suggested Citation

  • Wei Ding & Yu Zhou & Guangting Chen & Hongfa Wang & Guangming Wang, 2013. "On the 2‐MRS Problem in a Tree with Unreliable Edges," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:743908
    DOI: 10.1155/2013/743908
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/743908
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/743908?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. Pitu B. Mirchandani & Amedeo R. Odoni, 1979. "Locations of Medians on Stochastic Networks," Transportation Science, INFORMS, vol. 13(2), pages 85-97, May.
    2. Mary E. Helander & Emanuel Melachrinoudis, 1997. "Facility Location and Reliable Route Planning in Hazardous Material Transportation," Transportation Science, INFORMS, vol. 31(3), pages 216-226, August.
    3. Michael O. Ball & Feng L. Lin, 1993. "A Reliability Model Applied to Emergency Service Vehicle Location," Operations Research, INFORMS, vol. 41(1), pages 18-36, February.
    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. Hongfa Wang & Wei Ding, 2014. "Weighted Cache Location Problem with Identical Servers," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Abdallah W. Aboutahoun & Eman Fares, 2019. "On the Location of a Constrained k−Tree Facility in a Tree Network with Unreliable Edges," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).

    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. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    2. Barbara Anthony & Vineet Goyal & Anupam Gupta & Viswanath Nagarajan, 2010. "A Plant Location Guide for the Unsure: Approximation Algorithms for Min-Max Location Problems," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 79-101, February.
    3. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    4. Nelas, José & Dias, Joana, 2020. "Optimal Emergency Vehicles Location: An approach considering the hierarchy and substitutability of resources," European Journal of Operational Research, Elsevier, vol. 287(2), pages 583-599.
    5. Li, Xiaopeng & Ouyang, Yanfeng & Peng, Fan, 2013. "A supporting station model for reliable infrastructure location design under interdependent disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 80-93.
    6. Shabnam Rekabi & Ali Ghodratnama & Amir Azaron, 2022. "Designing pharmaceutical supply chain networks with perishable items considering congestion," Operational Research, Springer, vol. 22(4), pages 4159-4219, September.
    7. Su, Qiang & Luo, Qinyi & Huang, Samuel H., 2015. "Cost-effective analyses for emergency medical services deployment: A case study in Shanghai," International Journal of Production Economics, Elsevier, vol. 163(C), pages 112-123.
    8. O Berman & Z Drezner, 2003. "A probabilistic one-centre location problem on a network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 871-877, August.
    9. Ouyang, Yanfeng & Wang, Zhaodong & Yang, Hai, 2015. "Facility location design under continuous traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 18-33.
    10. Azcuy, Irecis & Agatz, Niels & Giesen, Ricardo, 2021. "Designing integrated urban delivery systems using public transport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    11. Afshartous, David & Guan, Yongtao & Mehrotra, Anuj, 2009. "US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1086-1096, August.
    12. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    13. Shariat-Mohaymany, Afshin & Babaei, Mohsen & Moadi, Saeed & Amiripour, Sayyed Mahdi, 2012. "Linear upper-bound unavailability set covering models for locating ambulances: Application to Tehran rural roads," European Journal of Operational Research, Elsevier, vol. 221(1), pages 263-272.
    14. Lawrence V. Snyder & Mark S. Daskin, 2005. "Reliability Models for Facility Location: The Expected Failure Cost Case," Transportation Science, INFORMS, vol. 39(3), pages 400-416, August.
    15. Nilay Noyan, 2010. "Alternate risk measures for emergency medical service system design," Annals of Operations Research, Springer, vol. 181(1), pages 559-589, December.
    16. Soo-Haeng Cho & Hoon Jang & Taesik Lee & John Turner, 2014. "Simultaneous Location of Trauma Centers and Helicopters for Emergency Medical Service Planning," Operations Research, INFORMS, vol. 62(4), pages 751-771, August.
    17. Michael K. Lim & Achal Bassamboo & Sunil Chopra & Mark S. Daskin, 2013. "Facility Location Decisions with Random Disruptions and Imperfect Estimation," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 239-249, May.
    18. An, Shi & Cui, Na & Bai, Yun & Xie, Weijun & Chen, Mingliu & Ouyang, Yanfeng, 2015. "Reliable emergency service facility location under facility disruption, en-route congestion and in-facility queuing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 199-216.
    19. Yun Bai & Xiaopeng Li & Fan Peng & Xin Wang & Yanfeng Ouyang, 2015. "Effects of Disruption Risks on Biorefinery Location Design," Energies, MDPI, vol. 8(2), pages 1-19, February.
    20. Boyacı, Burak & Geroliminis, Nikolas, 2015. "Approximation methods for large-scale spatial queueing systems," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 151-181.

    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:743908. 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.