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We study the Neighbor Aided Network Installation Problem (NANIP) introducedpreviously which asks for a minimal cost ordering of the vertices of a graph,where the cost of visiting a node is a function of the number of neighbors thathave already been visited. This problem has applications in resource managementand disaster recovery. In this paper we analyze the computational hardness ofNANIP. In particular we show that this problem is NP-hard even when restrictedto convex decreasing cost functions, give a linear approximation lower boundfor the greedy algorithm, and prove a general sub-constant approximation lowerbound. Then we give a new integer programming formulation of NANIP andempirically observe its speedup over the original integer program.

Network installation and recovery: approximation lower bounds and faster exact formulations