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

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.

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.

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.

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

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.

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 ??

Update propagation

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.

SCA example

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.

Direct query - example

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.

Adaptive querying 

Adapting query 

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.

Performance Evaluation Update costs

Performance Evaluation Query costs

Comparison with alternatives

Conclusion  Direct query  SCA query  Adaptive scheme