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An Efficient Clustering-based Heuristic for Data Gathering and Aggregation in Sensor Networks
Wireless Communications and Networking (WCNC 2003). IEEE , Volume: 3 , 16-20 March 2003. Koustuv Dasgupta, Konstantinos Kalpakis, Parag Namjoshi
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Outline System Model The Data Gathering Problem MLDA
Finding a near-optimal admissible flow network
Constructing a schedule CMLDA Experiment
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System Model sensor numbers <- n t <- the only one base station locations are fixed and known apriori round <- each time unit packet generating rate <- one data
packet per round all data packet size <- k bits transmission ability of each sensor <- to
any other sensor through the network or directly to the base station
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Energy Model A sensor consumes to run the transmitter
or receiver circuitry for the transmitter
amplifier Thus,
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The Data Gathering Problem We define lifetime T of the system to be
the number of rounds until the first sensor is drained of its energy
Data gathering schedule <- a collection of T directed trees, each rooted at the base station and spanning all the sensors
Objective: Find a schedule that maximizes the system
lifetime T
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MLDA: Maximum Lifetime Data gathering with Aggregation
Assumption: that an intermediate sensor can aggregate
multiple incoming packets into a single outgoing packet
fi,j <- total number of packets i transmits to j Energy Constraints:
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MLDA Flow network G = (V,E) <- a directed
graph where V <- all the nodes , E <- (i,j) with capacity fi,j whenever fi,j >0
Theorem 1:Let S be a schedule with lifetime T and G be the flow network induced by S
then (->)for each sensor s, the maximum flow from s to he base station t in G is >= TProve : Each packet from a sensor must reach the base station
Thus, a necessary condition for a schedule to have lifetime T is that each node in the induced flow network can push flow T to the base station t
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Solution of MLDA admissible flow network with lifetime T
1.allow each sensor to push flow T to base 2.respecting the energy constraints in (3)
optimal admissible flow network A admissible flow network with maximum
lifetime
First we find a near-optimal admissible flow network G
Then, we construct a schedule from G
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Finding a near-optimal admissible flow network
<- the flow k send to t over the edge (i,j)
//Energy constraint i
k k
k+T
//The flow k send out is T and will all arrive at t
Integer Program
NP complete
Linear Relaxation <- Polynomial time
Allow fractional values
We find G with
maximum T
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Schedule
Fig. 1. An admissible flow network G with lifetime 100 rounds, and two aggregation trees A1 and A2 with lifetimes 60 and 40 rounds respectively.
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Constructing a schedule Discuss how to get a schedule from an
admissible flow network f <- the life time of the aggregation tree Def 1: Given an admissible flow network
G with lifetime f ,we define the (A,f)-reduction G’ of G to be the flow network that result from G after reducing by f, the capacities of all of its edges that are also in A. We call G’ the (A,f)-reduced G.
Def 2: An (A,f)-reduction G’ of G is feasible if the maximum flow from v to the base station t in G’ is >= T – f for each vertex v in G’.
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Constructing a schedule If A is an aggregation tree, with lifetime
f, for an admissible flow network G with
lifetime T , and the (A,f)-reduction of G is feasible
Then (->) the (A,f)-reduced flow network G’ of G is
an admissible flow network with lifetime T-f
Therefore we can devise a simple iterative algorithm
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Fig. 2. Constructing aggregation tree A with lifetime f from an admissible flow network G with lifetime T.
//Aggregation Tree
Find a (i,j) that makes Gr feasible
//The running time of this algorithm is polynomial of nWe can prove that it is always possible to find a collection of aggregation trees based on a powerful theorem in graph theory
jiG
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CMLDA
Objective: The MLDA algorithm involves solving
a linear program with O(n^3) variables and constraints.
For large values of n, this can be computationally expensive.
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CMLDA – Clustering-based MLDA heuristic m <- numbers of clusters Øi <- ith cluster |Øi|<= c for i = 1,2,…,m super-sensor <- cluster εØi <- energy of cluster i <- total energy in
cluster i Distance between Øi and Øj <- the
maximum distance between any two nodes in each cluster
Base station defined as Øm+1 (with single node)
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CMLDA We can use previous method to find a
schedule consists of T1,T2,…,Tk, each rooted at Øm+1
AS-tree <- such aggregate tree (Aggregation super-tree)
<- residual energy at sensor I Initially = for all sensor
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CMLDA
We use BUILD-TREE procedure to construct an aggregation tree A from AS-tree
Objective: construct aggregation trees such that
minimum residual energy among the n sensors is maximized(thereby maximizing the lifetime)
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Pre-order Traversal
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BUILD-TREE procedure
Include all nodes in Ø to the required Aggregation Tree A
Def: residual energy of a pair (i,j) <-
Distance and Residual energy
update //pre-order
The running time of the procedure is O(n^3)There could be more than one AS-tree
We choose the AS-tree in decreasing order of their lifetimes
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Experiments R <- CMLDA lifetime / LRS lifetime Depth of a sensor v <- its average
depth in each of the aggregation trees D <- depth of the schedule <-
Give an estimate of the average delay that is incurred insending data packets to the base station
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Experiments
Initial Energy 1J , Packet size 1000 bits
Tradeoffs between delays and system lifetime
fractional
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ExperimentsWe cannot see the improvement in CMLDA compared to MLDA with the increasing network size
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Future Work Investigate modifications to the MLDA
algorithm that would allow sensor to be added to (or removed from) the network, without having to re-compute the entire schedule
Study the data gathering problem with depth (delay) constraints for individual sensors , in order to attain desired tradeoffs between the delay experienced by the sensors and the lifetime achieved by the system
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