EAI Endorsed Transactions on Energy Web 16(10): e5

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={16},
        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 [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.