Going Beyond Nodal Aggregates: Spatial Average of a Continuous Physical Process in Sensor Networks

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Going Beyond Nodal Aggregates Spatial Average of
a Continuous Physical Process in Sensor Networks

• Simon Han, Ganeriwal Saurabh,
• Mani Srivastava
• simonhan, saurabh, mbs_at_ee.ucla.edu)

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Outline (to be removed later)

• Introduction to aggregation
• Nodal aggregates
• Spatial aggregates
• Spatial Interpolation / Spatial Average
• Kriging Method
• Delaunay Triangulation
• Voronoi
• Analysis
• Centralized periodic
• Centralized snapshot
• Distributed periodic
• Simulation
• Process model
• Implementation
• Fortunes Voronoi package
• Dummy nodes placement
• Conclusion
• Thanks
• Heemin for Polygon clipping

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Aggregation

• Communication is expensive
• Compress data near source to reduce communication
  (e.g. max, average, etc)

MICA mote Berkeley
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Type of Aggregation

• Nodal aggregate
• E.g. number of nodes that has temperature greater
  than 30.
• Well studied in sensor network
• Suit for discrete data
• Spatial aggregate
• E.g. average temperature in the sensor network.
• Suit for continuous data
• The focus of this talk

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Design Space

• Aggregation possible
• Localized Distributed Algorithm
• Involve distance factor
• Physical phenomena
• Light weight
• Limited computation resource

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Spatial Interpolation Methods

• By Scope
• Global use all data points
• Local use limited set of data points
• By Fit
• Exact observed data points predicted exactly
• Approximated even observed data points predicted
  with error
• By Model
• Deterministic math model
• Stochastic probabilistic model

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IDW (Inverse Distance Weighting)

• Toblers Law
• In space, everything is related to everything
  else, but closer location more so.
• zx Si ?izi with Si ?i 1 or
• zx Si wizi / Si wi , wi 1/dix2
• Local, exact, deterministic
• i? accuracy? cost?
• Distributed?
• Point association problem

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Trend Surface

• The surface is approximated by a polynomial
  fitting to data points
• Global, approximated, stochastic
• Aggregation not possible

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Thiessen Polygons

• Also known as Voronoi polygons
• Collection of all points that are closer to known
  point than any other points
• Local, exact, deterministic
• May require global knowledge

Picture from http//skagit.meas.ncsu.edu/helena/g
mslab/viz/sinter.html
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Triangulated Irregular Network (TIN)

• Also known as Delaunay triangulation
• Models surface as a set of contiguous,
  non-overlapping triangles. Within each triangle
  the surface is represented by a plane.
• Local, exact, deterministic
• May require global knowledge

Picture from http//skagit.meas.ncsu.edu/helena/g
mslab/viz/sinter.html
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Kriging

• uses a semivariogram, a measure of spatial
  correlation between two points, so the weights
  change according to th e spatial arrangement of
  the samples.
• Local/global, exact, stochastic.

Picture from http//skagit.meas.ncsu.edu/helena/g
mslab/viz/sinter.html
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Implementation

• Straight port from simulation
• Steven Fortune Voronoi
• Polygon clipping
• Greens Polygon area
• Memory optimized
• Bisector node with each neighbor
• Dummy placements to handle clipping
• Greens Polygon area

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Varying diffusion model
Varying number of sources
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Varying mobility of sources
Robustness to link failures
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