On the Minimum Cost Range Assignment Problem

We study the problem of assigning transmission ranges to radio stations placed in a d-dimensional (d-D) Euclidean space in order to achieve a strongly connected communication network with minimum total cost, where the cost of transmitting in range r is proportional to \(r^\alpha \). While this problem can be solved optimally in 1D, in higher dimensions it is known to be NP-hard for any \(\alpha \ge 1\).