1. Construction of Optimal Data Aggregation Trees for Wireless Sensor Networks Deying Li, Jiannong Cao, Ming Liu, and Yuan Zheng Computer Communications and Networks 15th International Conference on15th International Conference on 2006

2. Outline 1. Introduction 2. Related Work 3. An Approximation Algorithm 4. Performance Evaluation 5. Conclusions

3. 1. Introduction Constructing trees for source nodes to send data to a single sink node A significant portion is for query dissemination and sensory data transmission if they consider data aggregation, there exists an optimal set of paths that form a tree

4. Intermediate nodes combine received data to compute an aggregated data Main goal – Minimize the number of non-source nodes in the tree to save energies

5. 2. Related Work Directed Diffusion was proposed as one of the basic paradigms Data-centric routing and application-specific processing such as data aggregation

6. Greedy Incremental Tree (GIT) (2002) – A shortest path is established for only the first source – Other sources is connected at the closest node on the existing tree

7. 3. An Approximation Algorithm Data collection request T for (s, P) – s is the sink node – P is a set of source nodes – T is a data aggregation tree Tree of total energy cost (send to parent)

8. Greedy Algorithm It constructs a multicast tree by iteratively adding source nodes to the existing tree T is a subgraph of G not including u, the distance d(u, T) is defined as

9. Input: G=(V,E) and {s} P (s = sink node and P V) Output: Multicast tree spanning on {s} P ------------------------------------------------------------------------------------------- Set T= {s}, Q= P While Q≠Φ Find u Q such that T = T {the shortest path between u and T} Q = Q - {u}

10. AT (Aggregation Tree) Algorithm Base on minimum spanning tree Three steps: 1. Construct a weighted complete graph on P 2. Compute a minimum spanning tree on the graph 3. The minimum spanning tree by the corresponding shortest path in the original graph

11. Step1: Weighted graph H= (P, E(P)) – P is the set of nodes –

12. Step2: Compute a minimum spanning tree T in H

13. Step3: Get an aggregation tree.

14. Distributed AT Algorithm Step 1: – Using the distributed algorithm in [17] to find all pairs shortest path in the network. Step 2: – The sink node can find minimum Steiner spanning tree on the multicast group

15. Five parts Part 1 – Find a spanning tree, T, of the un-weighted graph G. Part 2 – Each node determines the identities of its neighbors in the graph G. Part 3 – Determine the All-Pairs Shortest-Distance matrix.

16. Part 4 – Broadcast the All-Pairs Shortest-Distance matrix to the sink node. Part 5 – Sink node multicasts a message to every node of the multicast tree along the tree edges.

17. 4. Performance Evaluation Three objectives: a) To study the deviation of the results of the AT algorithm from the optimal algorithm using exhaustive search (OA) b) To study the scalability of the AT algorithm when the number of sensor nodes increases c) To compare the performance of the AT algorithm with the Greedy algorithm (GA)

18. 1000x1000 Allocating N nodes Transmission range R Select M nodes as sources

19. Comparing AT with OA N=50, and R=80, 100, 125, 150

20. The Scalability of AT algorithm R=80, 100, 120 and N=500, 1000

21. Comparing AT with GA when N=500 R=80, 100, 120 and N=500, 1000

22. Comparing AT with GA when N=1000

23. 5. Conclusions Save energies of as many non-source nodes Greedy algorithm and approximation algorithm can construct a data aggregation tree A good result approximation to the optimal tree

25. The distributed AT algorithm terminates in time A message complexity of