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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 have the following results: (a) In the one-dimensional case, with uniform [0, 1]-distributed distances, the expected approximation ratio is bounded above by 2–2/($p$+2), where $p$ denotes the distance power gradient. (b) For the complete graph, with uniform [0, 1] distributed edge weights, the expected approximation ratio is bounded above by 2- 1/2$\zeta$(3), where $\zeta$ denotes the Riemann zeta function

Average Case Analysis of the MST-heuristic for the Power Assignment Problem: Special Cases