Peer-to-Peer Spatial Queries in Sensor Networks

1. Peer-to-Peer Spatial Queries in Sensor Networks Murat Demirbas Hakan Ferhatosmanoglu The Ohio State University

2. Sensor networks • A sensor node: • 8K RAM, 4Mhz processor • magnetism, heat, sound, vibration, infrared • wireless communication up to 200 feet • costs ~$10 (right now costs $100) • Applications include: • ecology monitoring, precision agriculture • military and surveillance • In OSU, we developed a tracking service for DARPA-NEST • classify trespassers as car, soldier, civilian • report the tracking information to a base-station (laptop) for visualization

3. Spatial queries in sensor networks • The primary goal of sensor networks is to monitor spatial information about a region of interest • Nearest neighbor (NN) queries are essential : What is the location of the nearest data object to (x,y) ? • Database systems • R-tree for efficient execution of nearest neighbor queries

4. Challenges in sensor networks • energy constrained nodes, network contention : • programs should avoid excessive communication • centralized programs are not suitable • work in database systems not readily applicable • faults : • data is noisy • nodes fail in complex ways • on site maintenance is not feasible • self-healing programs are needed

5. P2P spatial queries in sensor networks • Pursuer- evader tracking • A pursuer should be able to query a node for the location of the closest evader • Every node is a peer : • each node (not only the base-station) can insert a query • each node can participate in the processing of the query • query is processed as local as possible

6. Our contributions We present a peer-to-peer query processing system where • only the relevant nodes for the correct execution of the query are involved in the query execution (for minimizing energy and response time) • the indexing structure, peer-tree, is self-stabilizing (for achieving eventually correct answers in the presence of faults)

7. Outline • Model • Peer-tree structure • P2P nearest neighbor queries • Pursuer – evader tracking revisited • Conclusions

8. Model • Geometric network model (2-D) • Connected graph; duplex links • Transient faults • Maximal parallelism in node actions

9. Outline • Model • Peer-tree structure • P2P nearest neighbor queries • Pursuer – evader tracking revisited • Conclusions

10. R-tree structure A . • Approximately balanced tree • A node holds n to 2n(c,mbr) pairs : • c is the child pointer • mbr is the minimum bounding rectangle (MBR) of all rectangles at c • Rectangles at any level may be overlapping • Every descending path in the tree is a sequence of nested rectangles with the last one containing the actual data B C F E D G H y A B D F G C E H x

11. Peer-tree construction • Hierarchical partitioning of a sensor network based on the number of nodes (n to 2n) contained at each cluster • every node cooperates at level 1 of the partitioning • only clusterheads of level i cooperate for level i+1 • Every node v maintains • l.v : highest level of construction v has cooperated • p.v(i),0<i=<l.v : parent of v at level i • c.v(i),0<i=<l.v : children of v at level i • mbr.v(i) : MBR of v(i) calculated using c.v(i) • Peer-tree is the tree that c pointers embed over the network • Two actions • Join/form cluster • Split a cluster

12. Join/form a cluster v executes a join/form cluster action if l.v=i yet p.v(i)=nil • v searches for a node with l= i+1, at increasingly larger radii : • if such a node is encountered v joins that node’s cluster • Else, if v encounters n nodes with l=i during its search : • v waits for a random time (to avoid formation of multiple clusters that are concurrently started by multiple nearby nodes) • if v is not contacted within this wait, v forms a cluster • p.v(i)=v, l.v=i+1, • c.v(i+1) is set, mbr.v(i+1) is calculated

13. Split cluster • During concurrent executions of join/form cluster action by multiple nodes, a level i clusterhead v may end up with > 2n children • v assigns extra level i clusterheads among its children and ensures that each cluster has n to 2n nodes

14. Peer-tree

15. Self-stabilization of peer-tree • v’s i’th level cluster is collapsed if: c.v(i)<n, or there is a node u in c.v(i) s.t., • u mbr.v(i), or • p.u  v • the nodes in the collapsed cluster join neighboring clusterheads or form their clusters

16. Outline • Model • Peer-tree structure • P2P nearest neighbor queries • Pursuer – evader tracking revisited • Conclusions

17. NN queries over traditional R-tree The search starts from the root (highest) level, and performs a traversal of the relevant MBRs • The MBRs that are guaranteed not to have the closest data point are pruned • e.g., MINDIST, the shortest possible distance from a point in an MBR to (x,y), is larger than the current candidate for NN • At every iteration, the algorithm • sorts the MBRs with respect to their MINDIST, • considers the first item in the list, expands its children, and inserts them to the list for processing

18. P2P NN queries over Peer-tree Any node in the network can submit an NN query concerning any coordinate (x,y) • If the query can be answered locally, there is no need to propagate it till the root (highest) level : • query is propagated up if (x,y) is not enclosed within current MBR • At some level a clusterhead that contains (x,y) is reached : • from this point on, the query is sent to children • children are ordered with respect to MINDIST • this way only the most relevant children are queried

19. NN query execution (x,y) query

20. NN query execution (x,y) query

21. P2P NN queries • If (x,y) is not within MBR of v at level i, mbr.v(i), then forward query to p.v(i) • let u be the first encountered clusterhead that contains (x,y) u forwards query to relevant children in c.u • While the query is traveling downwards, each clusterhead • sorts the children wrt MINDIST • prunes list using the replies from queried children • A level 0 node returns its nearest distance NN, reply is propagated up • u aggregates the replies • if (x,y) is encapsulated by c.u, the reply is sent to querying node • else, u punts the query to its clusterhead

22. NN query execution (x’,y’) query

23. Tradeoff : time vs. energy • Minimal response time • The clusterhead forwards the query to its relevant children in parallel (concurrent execution) • Minimal energy consumption • The clusterhead forwards the query to its relevant children sequentially (to maximize pruning) • Optimizing both • Hybrid of the above

24. Outline • Model • Peer-tree structure • P2P nearest neighbor queries • Pursuer – evader tracking revisited • Conclusions

25. Pursuer-evader problem • Evader is omniscient; Strategy of evader is unknown • Pursuer can only see state of nearest node; Pursuer moves faster than evader • Required is to design a program for nodes and pursuer so that pursuer can catch evader (despite the occurrence of faults) [Demirbas, Arora, Gouda]

26. Evader-centric program (cont.) • Tracking tree is dynamically rooted at the evader • Parent of a node is closer to the evader

27. Evader-centric program (cont.) • Tracking tree is dynamically rooted at the evader • Parent of a node is closer to the evader

28. Evader-centric program (cont.) • Tracking tree is dynamically rooted at the evader • Parent of a node is closer to the evader

29. Pursuer-evader tracking viaP2P spatial queries • The pursuer submits an NN query with its own location to find out the location of the nearest evader to itself • On demand approach • No tracking tree is maintained, a clusterhead is only aware of the existence of an evader in its region, but does not know where it is

30. Conclusions • We have presented for the first time a peer-to-peer spatial query processing system for sensor networks • We are implementing this system in the context of our work on tracking services for sensor network (LITS) • Indexing in database systems, peer-to-peer systems, sensor networks have a lot of similarities (as well as distinctions) • peer-tree is based on R-tree concept in database systems • possible to extend peer-tree for wired systems • since energy is no longer an issue, scalability and load balancing can be improved by inserting long links