ew 16(10): e5

Research Article

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

• @ARTICLE{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},
journal={EAI Endorsed Transactions on Energy Web},
volume={3},
number={10},
publisher={ACM},
journal_a={EW},
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
EW
EAI
DOI: 10.4108/eai.14-12-2015.2262699
Maurits de Graaf1,*, Richard Boucherie2, Johann Hurink2, Jan-Kees van Ommeren2
• 1: Thales Nederland B.V., University of Twente
• 2: University of Twente
*Contact email: M.deGraaf@utwente.nl

## 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.