Then the constraints are
a) At least one and no more than K CRegions are selected:
346 Kai-Wei Fan, Sha Liu, and Prasun Sinha
1???x ?? 1,
1???x ?· k.
b) Each sensor node must be connected with at least one CRegion:
Ax ?? 1.
c) If CRegion i is selected, minj should be less than or equal to hijxi. To
formulate this, it must be ensured that when CRegion i is not selected, minj
should not be set to 0. Thus the constraint is
minj ?· hijxi + mx???
i
where m is a constant larger than the maximum of hij ??™s.
Since m is the maximum of all minj ??™s, the objective function is
Y = MIN(1???m).
3. For a given bound mtotalhops on the total communication hops for all nodes to
reach their closest selected CRegions, minimize the number of gateways. The
formulation is the same as in the previous question except that the constraint
1x ?· k is replaced by
1???min ?· mtotalhops
where min = (min1, min2, . . . , minN)???.
The objective function is also changed to
Y = MIN(1???x).
4. For a given maximum number of gateways, find a placement such that the total
number of communication hops for all sensor nodes to reach their closest
selected gateways.
Based on the problem formulation of Problem 2, the constraint of m is removed
since the total number of hops are concerned instead of the maximum. Thus the
objective function is also changed to
Y = MIN(1???min).
8 Summary
Data Aggregation is an efficient mechanism as it not only reduces the energy consumption
of packet transmissions but also lowers the traffic load and therefore reduces
the contentions and collisions.
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