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

Outline System Model The Data Gathering Problem MLDA

Finding a near-optimal admissible flow network

Constructing a schedule CMLDA Experiment

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

Energy Model A sensor consumes to run the transmitter

or receiver circuitry for the transmitter

amplifier Thus,

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

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:

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

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

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

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.

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’.

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

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

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.

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)

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

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)

Pre-order Traversal

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

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

Experiments

Initial Energy 1J , Packet size 1000 bits

Tradeoffs between delays and system lifetime

fractional

ExperimentsWe cannot see the improvement in CMLDA compared to MLDA with the increasing network size

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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