Research Article
Average Case Analysis of the MST-heuristic for the Power Assignment Problem: Special Cases
@INPROCEEDINGS{10.4108/eai.14-12-2015.2262699, author={Maurits de Graaf and Richard Boucherie and Johann Hurink and Jan-Kees van Ommeren}, title={Average Case Analysis of the MST-heuristic for the Power Assignment Problem: Special Cases}, proceedings={9th EAI International Conference on Performance Evaluation Methodologies and Tools}, publisher={ACM}, proceedings_a={VALUETOOLS}, year={2016}, month={1}, keywords={power assignment minimum spanning tree random graphs}, doi={10.4108/eai.14-12-2015.2262699} }- Maurits de Graaf
Richard Boucherie
Johann Hurink
Jan-Kees van Ommeren
Year: 2016
Average Case Analysis of the MST-heuristic for the Power Assignment Problem: Special Cases
VALUETOOLS
ICST
DOI: 10.4108/eai.14-12-2015.2262699
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 $\left[ 0,1 \right]$-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 $2-1/2\zeta(3)$, where $\zeta$ denotes the Riemann zeta function.
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