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Energy-Efficient Paths in Radio Networks

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Abstract

We consider a radio network consisting of n stations represented as the complete graph on a set of n points in the Euclidean plane with edge weights ω(p,q)=|pq|δ+C p , for some constant δ>1 and nonnegative offset costs C p . Our goal is to find paths of minimal energy cost between any pair of points that do not use more than some given number k of hops.

We present an exact algorithm for the important case when δ=2, which requires \(\mathcal {O}(kn\log n)\) time per query pair (p,q). For the case of an unrestricted number of hops we describe a family of algorithms with query time \(\mathcal {O}(n^{1+\alpha})\), where α>0 can be chosen arbitrarily. If we relax the exactness requirement, we can find an approximate (1+ε) solution in constant time by querying a data structure which has linear size and which can be build in \(\mathcal {O}(n\log n)\) time. The dependence on ε is polynomial in 1/ε.

One tool we employ might be of independent interest: For any pair of points (p,q)∈(P×P) we can report in constant time the cluster pair (A,B) representing (p,q) in a well-separated pair decomposition of P.

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, 66123, Saarbrücken, Germany

    Rene Beier, Stefan Funke & Domagoj Matijević

  2. Fakultät für Informatik, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Peter Sanders

Authors
  1. Rene Beier
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  2. Stefan Funke
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  3. Domagoj Matijević
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  4. Peter Sanders
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Corresponding author

Correspondence to Domagoj Matijević.

Additional information

Preliminary versions of parts of the results described here were already published in the proceeding of 11th Annual European Symposium on Algorithms (see [16]) and the proceeding of 29th International Colloquium on Automata, Languages and Programming (see [5]).

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Beier, R., Funke, S., Matijević, D. et al. Energy-Efficient Paths in Radio Networks. Algorithmica 61, 298–319 (2011). https://doi.org/10.1007/s00453-010-9414-0

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  • DOI: https://doi.org/10.1007/s00453-010-9414-0

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