Sequential construction of costly networks

Natural disasters or attacks often disrupt infrastructure networks requiring a costly recovery. This motivates an optimization problem where the objecitve is to construct the nodes of a graph G(V;E), and the cost of each node is dependent on the number of its neighbors previously constructed, or more generally, any properties of the previously-completed subgraph. In this optimization problem the objective is to find a permutation of the nodes which results in the least construction cost. We prove that in the case where the cost of nodes is a convex function in the number of neighbors, the optimal construction sequence is to start at a single node and move outwards. We also introduce algorithms and heuristics for solving various instances of the problem. Those methods can be applied to help reduce the cost of recovering from disasters as well as to plan the deployment of new network infrastructure.