1. Rate-based Data Propagation in Sensor Networks Gurdip Singh and Sandeep Pujar Computing and Information Sciences Sanjoy Das Electrical and Computer Engineering Kansas State University WCNC 2004 Speaker: Hao-Chun Sun

2. Outline  Introduction  Rate-based Tree (RBT) Algorithm Breadth-First tree based algorithm (BFS) Single phase Algorithm (SPA)  Performance Evaluation  Conclusion and Future Work

3. Introduction -background-  Sensor networks Small and cheap computational nodes Such nodes can sense and communication data to potential consumer nodes. Monitor traffic movements Application  One or one more operators may be interested in queries.  Different operators may be interested in knowing this information at different sampling rates.

4. Introduction -motivation-  The problem of constructing rate-based trees (RBT) A single source s and a set of destination D Each d in D specifies the rate r d To construct an optimal multicast tree with s as the root such that each destination gets data at the desired rate. Optimal multicast tree has the lowest cost. NP-complete problem

5. Rate-based Tree (RBT) Algorithm  Several variants of the general problem Un-weight graphs  Breadth-First Tree based algorithm (BFS)  Single phase algorithm (SPA) Weight graphs  SPA_W algorithm

6. Rate-based Tree (RBT) Algorithm  RBT Problem Definition Network: G=(N,E)  N: nodes  E: edges, representing the communication links A single source node s and a set of destinations D  Destination i is interested in obtaining information at rate r i from the source. All nodes are destinations

7. Rate-based Tree (RBT) Algorithm  RBT Problem Definition RBT must to satisfy two properties  For each node i with parent edge e, r e ≧ r i  For each node i, the rate assigned to its parent edge must be greater than or equal to r i and the rate of any of its outgoing edges. Pi i riri rere r o1 r o2

8. Rate-based Tree (RBT) Algorithm  An example of rate-based Trees g a bc d e f 10 8 5 5 0 0 8 8 8 5

9. Rate-based Tree (RBT) Algorithm  An example of rate-based Trees g a bc d e f 10 8 5 5 0 0 8 5 8 5

10. Rate-based Tree (RBT) Algorithm  Two metric to evaluate the algorithms The cost of the RBT  The sum of the cost of all tree edges Cost = w (i, j) × r e, where e is the edge from i to j. The number of messages sent in and execution of the algorithm. g g g g g g g g 10 8 8 5 8 8 5 8 5 Cost (A)=10+8+8+8+5 Cost (B)=10+8+8+5+5 Cost (A)=10+8+8+8+5 Cost (B)=10+8+8+5+5 (A) (B)

11. Rate-based Tree (RBT) Algorithm  Un-weighted graphs Breadth-First Tree based algorithm (BFS) —  BFS tree construction algorithm Along the path to the root is shortest path for un-weighted graphs Sum of the weight along the path to the root is minimal for weighted graphs.  Label the edges rules

12. Rate-based Tree (RBT) Algorithm  Un-weighted graphs Breadth-First Tree based algorithm (BFS) — a b e c d 5 20 40 20 label(20) label(40) label(20) label(40) 20 40 a b e c d 5 20 40 20 label(20) label(40) label(5) label(40) 5 20 40

13. Rate-based Tree (RBT) Algorithm  Un-weighted graphs A Single Phase Algorithm (SPA) — a f d b c e 5 10 5 5 explore(0) explore(5) Ack(5) Ack(10) explore(5) Ack(10) explore(10) Ack(10) explore(5) Ack(5) update(10) 5 5 5 10 update(10) Nack

14. Rate-based Tree (RBT) Algorithm  Un-weighted graphs A Single Phase Algorithm (SPA) — a f d b c e 5 10 5 5 5 5

15. Rate-based Tree (RBT) Algorithm  Weighted graphs SPA_W algorithm —  Modify switching parent rules When node i receive an explore (r) message form j.  r ≧ r i and r > r pi  r i × cost (i, j) < r i × cost (i, Pi) j i Pi explore(r) cost (i, j) cost (i, Pi)

16. Performance Evaluation  Discrete event simulation  Network Topologies were generated by randomly placing N nodes in a M×M matrix.  The probability of two nodes being neighboring is inversely proportional to the distance between them.  N is ranging from 20 to 160.

17. Performance Evaluation  Tree cost for SPA vs. BFS

18. Performance Evaluation  Number of messages for SPA vs. BFS

19. Performance Evaluation  Number of messages for different rate groups

20. Performance Evaluation  Weighted Tree Cost

21. Conclusion and Future Work  This paper presented algorithms for rate-based propagation of data in sensor network.  The paper addresses the problems where consumers of data may be requesting the data from the same source at different rates and needing to construct a data propagation tree that satisfies all requested rate.  It presented an efficient algorithm and studied several of its variants.

22. Conclusion and Future Work  We will consider the case of internal nodes are not destination nodes.  An interesting variation is the case when are multiple data items and multiple producers and the consumers in obtaining data items.  We plan to study dynamic changes to the rates at which consumers are subscribing.