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Convert a sensor with m-data unit to m virtual sensors with 1-data unit each.

Convert a sensor with m-data unit to m virtual sensors with 1-data unit each.

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Article
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This paper studies the wireless sensor networks (WSN) application scenario with periodical traffic from all sensors to a sink. We present a time-optimum and energy-efficient packet scheduling algorithm and its distributed implementation. We first give a general many-to-one packet scheduling algorithm for wireless networks, and then prove that it is...

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Context 1
... 5: Given a sink tree T (u 0 ) with t branches Proof: For each sensor u i with d u i data units, we generate m = d u i virtual-sensors {u 1 i , u 2 i , · · · , u m i } with one data unit each, as illustrated in Figure 3. Among them, u 1 i replaces u i to connect all its original children {u i+1 } and parent u i−1 , and each virtual sensor u j i (j ∈ [2, m]) becomes the new children of u i−1 . ...
Context 2
... first assume all direct children of a sink have only one unit of data. Then, it is not difficult to calculate that Algorithm 2 takes max(2DN (u 1 ) − 1, DN (u 0 ) − 1) time slots to collect all the data in the sensor network, since each sensor u i in Figure 3(a) can be converted to d u i vir- tual sensors and each virtual-sensor in the new tree has the same amount of data. Then Theorem 4 applies directly. ...

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... The problem of minimizing the scheduling length for raw-data convergecast, using the interference graph, is proved to be NP-complete by a reduction from the known hard problem, Partition Problem [33]. The optimum lower bounded max(2n − 1 , N) is obtained by the algorithm of [34], where represents the number of nodes in the network and represents the maximum number of nodes in a top-subtree (subtree that has a child of the sink as its root). But this optimum is for radios with fixed bandwidth. ...
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