Low-Energy Fault-Tolerant Bounded-Hop Broadcast in Wireless Networks

This paper studies asymmetric power assignments in wireless ad hoc networks. The temporary, unfixed physical topology of wireless ad hoc networks is determined by the distribution of the wireless nodes as well as the transmission power (range) assignment of each node. We consider the problem of
bounded-hop

broadcast
under
k-fault

resilience
criterion for linear and planar layout of nodes. The topology that results from our power assignment allows a broadcast operation from a wireless node
r
to any other node in at most
h
hops and is
k
-fault resistant. We develop simple approximation algorithms for the two cases and obtain the following approximation ratios: linear case-
O
(
k
); planar case-we first prove a factor of
O
(
k

³
) , which is later decreased to
O
(
k

²
) by a finer analysis. Finally, we show a trivial power assignment with a cost
O
(
h
) times the optimum. To the best of our knowledge, these are the first nontrivial results for this problem.