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#### Power assignment problems in wireless communication

##### MPS-Authors
/persons/resource/persons44464

Funke,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons44893

Laue,  Sören
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45109

Naujoks,  Rouven
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Fulltext (public)

MPI-I-2006-1-004.pdf
(Any fulltext), 177KB

##### Supplementary Material (public)
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##### Citation

Funke, S., Laue, S., Naujoks, R., & Zvi, L.(2006). Power assignment problems in wireless communication (MPI-I-2006-1-004). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6820-E
##### Abstract
A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; for example one problem studied before in (Vittorio Bil{\o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) and (Helmut Alt et al.: Minimum-cost coverage of point sets by disks, SCG 2006) aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bil{\o} et al. (see Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) to $O\left( n+ {\left(\frac{k^{2d+1}}{\epsilon^d}\right)}^{ \min{\{\; 2k,\;\; (\alpha/\epsilon)^{O(d)} \;\}} } \right)$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts.