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.

在 Averbakh 和 Pereira (IIE Trans 44(8):681–694, 2012; Eur J Oper Res 244:715–729, 2015) 中介绍的网络构建/恢复问题中，服务器（施工人员）构建给定网络的边缘从给定的顶点（仓库）开始，以恒定的构建速度。服务器可以在已经构建好的网络部分中以比构建速度更快的速度运行。顶点的恢复时间是顶点通过已​​经构建的路径连接到仓库的时间。截止日期和/或权重与顶点相关联。需要找到使总加权恢复时间或顶点的最大延迟最小化的最佳施工进度表。众所周知，这两个问题在树上都是多项式可解的，在一般网络上是 NP-hard 的。