Network construction/restoration problems: cycles and complexity

Tianyu Wang () and Igor Averbakh ()
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Tianyu Wang: Beihang University
Igor Averbakh: University of Toronto Scarborough

Journal of Combinatorial Optimization, 2022, vol. 44, issue 1, No 3, 73 pages

Abstract: 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.

Keywords: Combinatorial optimization; Network construction; Scheduling; Computational complexity (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00813-2

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