@techreport{escidoc:1819172,
TITLE = {Power assignment problems in wireless communication},
AUTHOR = {Funke, Stefan and Laue, S{\"o}ren and Naujoks, Rouven and Zvi, Lotker},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2006-1-004},
NUMBER = {MPI-I-2006-1-004},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {2006},
DATE = {2006},
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.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}