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Published in:
2006 | OriginalPaper | Chapter
Recent Advances on Approximation Algorithms for Minimum Energy Range Assignment Problems in Ad-Hoc Wireless Networks
Author : David Peleg
Published in: Combinatorial and Algorithmic Aspects of Networking
Publisher: Springer Berlin Heidelberg
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Ad-hoc wireless networks have no wired infrastructure. Instead, they consist of a collection of radio stations
S
={1,2,...,
n
} deployed in a given region and connected by wireless links. Each station is assigned a transmission range, and a station
t
can correctly receive the transmission of another station
s
if and only if
t
is within the range of
s
. The overall range assignment,
r
:
S
→
R
+
, determines a (directed) transmission graph
G
r
. The transmission range of a station depends on the energy invested by the station. In particular, the power
P
s
required by a station
s
to correctly transmit data to another station
t
must satisfy the inequality
$P_s \ge {\tt dist}(s,t)^{\alpha}$
, where
dist
(
s
,
t
) is the Euclidean distance between
s
and
t
and
α
≥1 is the
distance-power gradient
. The value of
α
may vary from 1 to more than 6 depending on the environment conditions at the location of the network (see [16]).