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

We study the Neighbor Aided Network Installation Problem (NANIP) introduced previously 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 that have already been visited. This problem has applications in resource management and disaster recovery. In this paper we analyze the computational hardness of NANIP. In particular we show that this problem is NP-hard even when restricted to convex decreasing cost functions, give a linear approximation lower bound for the greedy algorithm, and prove a general sub-constant approximation lower bound. Then we give a new integer programming formulation of NANIP and empirically observe its speedup over the original integer program.