It is easy to find that the transmission cost would grow with the increase of
the density of deployed nodes. In [1], the authors discuss possible techniques
for boundary detection which rely on the measurements from the neighboring
nodes within a probing radius R. It is also mentioned that the accuracy could
be improved by increasing the radius R. A distributed scheme requires message
transmission among all the nodes within R, so the computation cost would be
increased by O(R2). If a hierarchical framework is used, the transmission between
two di?®erent clusters would only require messages between the two clusterheads
rather than all the messages between each pair (two nodes in the two
di?®erent clusters). For example, we have two clusters A = a0, a1, . . . , am and
B = b0, b1, . . . , bn, where a0 and b0 are the clusterheads of the corresponding
cluster. Simply, in a hierarchical framework, we only need a0 () b0 messages.
But in the distributed manner, we would need ai () bj , 0 ?· i ?· m, 0 ?· j ?· n
messages. So the cost of transmission would be decreased by m ?— n.
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Chapter 6 Boundary Detection for Sensor Networks
5.2 Dyadic Partition Algorithm
In [4], the author introduces a hierarchical structure of ???clusterheads??? which
aggregates information from children nodes (might be also clusterheads if they
are in the medium level) and then passes signal estimates to the upper layer in
the hierarchy.
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