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

Maurits de Graaf; Richard Boucherie; Johann Hurink; Jan-Kees van Ommeren

Research Article

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

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@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.

Keywords: power assignment, minimum spanning tree, random graphs

Published: 2016-01-04
Publisher: ACM

: http://dx.doi.org/10.4108/eai.14-12-2015.2262699

Copyright © 2015 M. de Graaf et al., licensed to EAI. This is an open access article distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unlimited use, distribution and reproduction in any medium so long as the original work is properly cited.