Energy-Efficient Paths in Radio Networks

We consider a radio network consisting of n stations represented as the complete graph on a set of n points in the Euclidean plane with edge weights ω(p,q)=|pq| ^δ +C _p , for some constant δ>1 and nonnegative offset costs C _p . Our goal is to find paths of minimal energy cost between any pair of points that do not use more than some given number k of hops.