An Efficient Clustering-based Heuristic for Data Gathering and Aggregation in Sensor Networks

1. 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

2. Outline • System Model • The Data Gathering Problem • MLDA • Finding a near-optimal admissible flow network • Constructing a schedule • CMLDA • Experiment

3. 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

4. Energy Model • A sensor consumes • to run the transmitter or receiver circuitry • for the transmitter amplifier • Thus,

5. 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 gatheringschedule <- 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

6. 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:

7. 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 >= T 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 Prove : Each packet from a sensor must reach the base station

8. 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

9. Finding a near-optimal admissible flow network <- the flow k send to t over the edge (i,j) We find G with maximum T Linear Relaxation <- Polynomial time Allow fractional values Integer Program NP complete //Energy constraint k k i +T k //The flow k send out is T and will all arrive at t

10. 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.

11. 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’.

12. 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

13. //Aggregation Tree G i j Find a (i,j) that makes Gr feasible //The running time of this algorithm is polynomial of n We can prove that it is always possible to find a collection of aggregation trees based on a powerful theorem in graph theory Fig. 2. Constructing aggregation tree A with lifetime f from an admissible flow network G with lifetime T.

14. 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.

15. 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)

16. 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

17. 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)

18. Pre-order Traversal

19. BUILD-TREE procedure Distance and Residual energy Include all nodes in Ø to the required Aggregation Tree A Def: residual energy of a pair (i,j) <- 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

21. 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 in sending data packets to the base station

22. Experiments Initial Energy 1J , Packet size 1000 bits fractional Tradeoffs between delays and system lifetime

23. Experiments We cannot see the improvement in CMLDA compared to MLDA with the increasing network size

24. 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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