Since in
the localized algorithms each node communicates only with other nodes in
some neighborhood, the communication overhead scales well with increase in
network size. For a similar reason, these algorithms are robust to network partitions
and node failures. Specifically for topology control, it is preferred that
the underlying network topology can be constructed in a localized manner.
Here a distributed algorithm constructing a graph G is a localized algorithm
if every node u can exactly decide all edges incident on u based only on the
information of all nodes within a constant hop of u.
1.3 Organization
The rest of the chapter is organized as follows. In Section 2, we survey several
geometry spanners that can be used as power-e?±cient topology for wireless
sensor networks. In Section 3, we review several low-weight structures that
are suitable for broadcasting in wireless sensor networks. In Section 4, state
of the art of constructing virtual backbone for sensor networks is reviewed. As
there are many heuristics proposed in this area, we concentrate on the ones
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Yu Wang
that have theoretic performance guarantees. Section 5 describes some other
related research issues on topology control for sensor networks. Finally, the
chapter concludes with Section 6.
2 Geometrical Spanners
As we mentioned before, when each node knows its geometrical position, the
geometry techniques can be applied in protocol design for sensor networks to
achieve better performance.
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