An average case analysis of the minimum spanning tree heuristic for the power assignment problem: DE GRAAF et al..

We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst-case approximation ratio of this heuristic is 2. We show that in Euclidean d-dimensional space, when the vertex set consists of a set of i.i.d. uniform random independent, identically distributed random variables in [0,1](d), and the distance power gradient equals the dimension d, the minimum spanning tree-based power assignment converges completely to a constant depending only on d.