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

Abstract

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-dimension-al case, with uniform [0, 1]-distributed distances, the expected approximation ratio is bounded above by $2 - 2/(\myp+2)$, where $\myp$ 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 / 2ζ(3), where ζ denotes the Riemann zeta function.

Keywords

• power assignment
• minimum spanning tree
• random graphs