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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. Igor Averbakh & Jordi Pereira, 2012. "The flowtime network construction problem," IISE Transactions, Taylor & Francis Journals, vol. 44(8), pages 681-694.
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