DIST: A Distributed Spatio-temporal Index Structure for Sensor Networks

1. Anand Meka and Ambuj Singh UCSB, 2005 DIST: A Distributed Spatio-temporal Index Structure for Sensor Networks

2. Introduction • Address the problem of plume tracking (in general, tracking of a mobile object) in a sensor network. • Design an analytical model to evaluate the expected cost based on the query location, query size and plume distribution.

3. Spatio-temporal Indexing • The sensor network is hierarchically decomposed into levels and a quad-tree partitioning (called cells) at each level. • A distributed indexing scheme exploits the plume's locality in space and time using a hierarchical index.

4. Spatial decomposition of the network

5. Spatial decomposition of the network • A plume can be mapped to a specific set of cells S at level α that contains it. • α and S can change dynamically as in α(t) and S(t)‏ • α does not change by more than one in two consecutive time instants. • The plume does not skip across the neighbors of a cell between two consecutive time instants.

6. Q:[42,65] X [42,48] X [t5, t11] • Return F, G

7. Shape summaries & update propagation • Every leader stores an index or a set of disjoint time intervals over which the plume was inside its cell. Each time interval has a begin and an end time instant such as [t1,t2]. • Assume that a plume's shape is continuously tracked and stored at specific sensor nodes called repository nodes.

8. Information maintaining • At each time instant t, a repository node senses the plume and computes α(t) and S(t). • How can the repository node know the α and S ?? • A repository node sends a message (id,t) to the leader of each cell c in S(t). • l(c) updates information. • Any neighboring cell d of c that had an open index at time t-1 ends its most recent time interval by inserting t-1. • Who notify those cells ??

9. Update propagation

10. Range Query Algorithm - SCA • Smallest Common Ancestor algorithm • The query originator determine the spatial cells at the level ε that are intersected by the query. • Determines the smallest common ancestor sca of these cells. • Transmits the query to the sca using an GPSR.

11. SCA example

12. Direct query algorithm • Query originator decomposes the query's spatial extent into cells at level ε, and directly queries these cells and all their ancestors. • Constructing a spanning tree (ST) at each level. • The query originator constructs a communication graph and finds a ST.

13. Direct query - example

14. Adaptive querying • Both the SCA and Direct query algorithms have their advantages and disadvantages. • SCA is effective in the case of a query with a large spatial range. • Direct query – small spatial extent • Adopting the better of the two schemes depending on the query location, query size, and plume distribution on a per-query basis.

15. Adaptive querying

16. Adapting query

17. Performance Evaluation • Simulation and mobility models • Cloud model: the centre of mass of the plume performs a random walk. • Gaussian plume dispersion model: the concentration of the plume perpendicular to the direction of the wind velocity follows a Gaussian distribution.

18. Performance Evaluation • Update costs

19. Performance Evaluation • Query costs

25. Comparison with alternatives

26. Comparison with alternatives

27. Conclusion • Direct query • SCA query • Adaptive scheme