Power Assignment Problems in Wireless Communication
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 \cite{Carrots, Bilo} 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+ϵ)
-approximate solution for this problem from
n
((α/ϵ
)
O(d)
)
as reported by Bilo et al. (\cite{Bilo}) to
O(n+
(
k
2d+1
ϵ
d
)
min{2k,(α/ϵ
)
O(d)
}
)
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.