Finally, we briefly discussed some other
research issues in topology control for sensor networks. Due to the space limit,
we did not give all of the detailed algorithms, proofs, and simulation results
for most protocols reviewed here. For more detail, refer to the references.
Though topology control has attracted considerable attention and been heavily
studied recently, there are still many open problems and we still believe
that the topology control is one primary challenge and plays an important
role in research of wireless sensor networks.
Some open problems and potential future work are listed as follows.
1. Though [42, 43] proved the sparsified Yao graph is a power spanner, it is
still open whether it is a length spanner for general graphs.
2. Is there a localized method or an easier way than the method in [56] to
build a bounded-degree planar spanner with low weight locally?
3. In this chapter, we assumed that the emission power is the major component
of the power consumption. However, in many cases, the emission
power is at the same level of the power needed for being idle or to receive
messages. It is then necessary to design new topologies under the new
energy model when the receiving power is not negligible.
4. As we mentioned before, practically, the networks are never so perfect as
unit disk graphs. It is very interesting (and hard) to study how to design
topology for more complex models than UDG which may consider the
impact of radio irregularity.
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