Sensor networks consist of a set
of sensor nodes which are spread over a geographical area. These nodes are
able to perform processing as well as sensing and are additionally capable of
communicating with each other.With coordination among these sensor nodes,
the network together will achieve a larger sensing task both in urban environments
and in inhospitable terrain. The sheer numbers of these sensors, the
limited resources on each sensor, and the expected dynamics in these environments
present unique challenges in the design of wireless sensor networks.
Topology control is one primary challenge in these scenarios. Unlike the
wired networks that typically have fixed network topologies, each sensor node
in a sensor network can potentially change the network topology by adjusting
its transmission range and/or selecting specific nodes to forward its messages,
thus, controlling its set of neighbors. The primary goal of topology control
in wireless sensor networks is to maintain network connectivity and optimize
network lifetime and throughput. In this chapter, we will survey various techniques
used for topology control in wireless sensor networks from a theoretical
perspective. First, we will discuss how to use geometrical position information
to design power-e?±cient network topologies, such as geometrical spanners
(which are power-e?±cient for routing) and geometrical low-weight structures
(which are power-e?±cient for broadcasting).
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