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Network construction/restoration problems: cycles and complexity

Author

Listed:
  • Tianyu Wang

    (Beihang University)

  • Igor Averbakh

    (University of Toronto Scarborough
    University of Toronto)

Abstract

In network construction/restoration problems introduced in Averbakh and Pereira (IIE Trans 44(8):681–694, 2012; Eur J Oper Res 244:715–729, 2015), a server (construction crew) builds edges of a given network starting from a given vertex (the depot), with a constant construction speed. The server can travel within the already constructed part of the network with a speed that is incomparably faster than the construction speed. The recovery time of a vertex is the time when the vertex becomes connected to the depot by an already constructed path. Due dates and/or weights are associated with vertices. It is required to find an optimal construction schedule that minimizes the total weighted recovery time or the maximum lateness of the vertices. Both problems are known to be polynomially solvable on trees and NP-hard on general networks. We prove that both problems are NP-hard even on so simple extensions of trees as cactuses, and discuss some polynomially solvable cases.

Suggested Citation

  • Tianyu Wang & Igor Averbakh, 2022. "Network construction/restoration problems: cycles and complexity," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 51-73, August.
  • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00813-2
    DOI: 10.1007/s10878-021-00813-2
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    References listed on IDEAS

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    1. Igor Averbakh & Jordi Pereira, 2018. "Lateness Minimization in Pairwise Connectivity Restoration Problems," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 522-538, August.
    2. Ajam, Meraj & Akbari, Vahid & Salman, F. Sibel, 2019. "Minimizing latency in post-disaster road clearance operations," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1098-1112.
    3. Igor Averbakh & Jordi Pereira, 2012. "The flowtime network construction problem," IISE Transactions, Taylor & Francis Journals, vol. 44(8), pages 681-694.
    4. Fu, Liping & Trudel, Mathieu & Kim, Valeri, 2009. "Optimizing winter road maintenance operations under real-time information," European Journal of Operational Research, Elsevier, vol. 196(1), pages 332-341, July.
    5. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    6. Baxter, Matthew & Elgindy, Tarek & Ernst, Andreas T. & Kalinowski, Thomas & Savelsbergh, Martin W.P., 2014. "Incremental network design with shortest paths," European Journal of Operational Research, Elsevier, vol. 238(3), pages 675-684.
    7. Nurre, Sarah G. & Cavdaroglu, Burak & Mitchell, John E. & Sharkey, Thomas C. & Wallace, William A., 2012. "Restoring infrastructure systems: An integrated network design and scheduling (INDS) problem," European Journal of Operational Research, Elsevier, vol. 223(3), pages 794-806.
    8. Anantaram Balakrishnan & Thomas L. Magnanti & Joel S. Sokol & Yi Wang, 2002. "Spare-Capacity Assignment For Line Restoration Using a Single-Facility Type," Operations Research, INFORMS, vol. 50(4), pages 617-635, August.
    9. Anantaram Balakrishnan & Thomas Magnanti & Joel Sokol & Yi Wang, 2001. "Telecommunication Link Restoration Planning with Multiple Facility Types," Annals of Operations Research, Springer, vol. 106(1), pages 127-154, September.
    10. Nihal Berktaş & Bahar Yetiş Kara & Oya Ekin Karaşan, 2016. "Solution methodologies for debris removal in disaster response," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(3), pages 403-445, September.
    11. Averbakh, Igor & Pereira, Jordi, 2015. "Network construction problems with due dates," European Journal of Operational Research, Elsevier, vol. 244(3), pages 715-729.
    12. Melih Çelik & Özlem Ergun & Pınar Keskinocak, 2015. "The Post-Disaster Debris Clearance Problem Under Incomplete Information," Operations Research, INFORMS, vol. 63(1), pages 65-85, February.
    13. Matteo Fischetti & Gilbert Laporte & Silvano Martello, 1993. "The Delivery Man Problem and Cumulative Matroids," Operations Research, INFORMS, vol. 41(6), pages 1055-1064, December.
    14. Willem E. de Paepe & Jan Karel Lenstra & Jiri Sgall & René A. Sitters & Leen Stougie, 2004. "Computer-Aided Complexity Classification of Dial-a-Ride Problems," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 120-132, May.
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