Then, we will review methods
to build hierarchical structures, virtual backbones, e?±ciently for sensor networks.
Finally, we will also briefly introduce other research issues on topology
control such as fault tolerance, interference, transmission power assignment
and power management. Due to the space limit, we can not cover all research
issues and methods in topology control. Thus, we will mainly focus on how to
build geometric structures and virtual backbones for wireless sensor networks.
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Yu Wang
1.1 Network Models and Assumptions
In the literature, people usually use a unit disk graph to model a sensor network.
Consider a sensor network consisting of a set V of n wireless sensor
nodes distributed in a two-dimensional plane. Each wireless sensor node has
an omni-directional antenna, so that a single transmission of a node can be
received by all nodes within its vicinity which, we assume, is a disk centered at
the node. We call the radius of this disk the transmission range of this sensor
node. By a proper scaling, we assume that all nodes have the maximum transmission
range equal to one unit. Two nodes within each other??™s transmission
ranges can communicate directly, while two far away nodes can communicate
through multi-hop wireless links by using intermediate nodes to relay the message.
These wireless sensor nodes define a unit disk graph UDG(V ) in which
there is an edge between two nodes if and only if their Euclidean distance is
at most 1.
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