Accordingly, after the first duration, the root node hears the partial aggregation
sent by its child nodes one hop away. After the second interval, the root
gets the partial aggregation from the nodes one and two hops away, and so
forth. After the kth interval, the root gets the partial aggregation from the
child nodes less than k ??’ 1 hops away. When the nodes that do not receive
the aggregate request receive the partial results from other nodes, they will
send the partial results to the nodes that are on the upper level.
Fig. 15. Pipelined aggregate [12].
Not only does this tend to include the nodes that would have been excluded
from a single pass aggregate, but the pipelined aggregate technique also has
two interesting properties. First, after aggregates have been reported by the
leaf nodes, new aggregates will arrive every i seconds. The value of i is very
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Chapter 12 Data Management in Sensor Networks
small. It is about the time it takes for a sensor to produce and transmit
a value. Second, assume the total time for an aggregation request to reach
the leaf nodes and return to the root is about t. Then, the root node starts
to get the first approximate aggregation after interval t and then it receives
additional aggregations every i seconds. According to the above properties, the
pipelined aggregation can provide users an aggregate stream. Since the stream
can reveal the change of the sensor data or the sensor network, generally, it is
more significant than a single aggregate value.
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