Random Structures & Algorithms

An average case analysis of the minimum spanning tree heuristic for the power assignment problem

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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 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.

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