Coverage Problems in Wireless Adhoc Sensor Networks

1
Coverage Problems in Wireless Ad-hoc Sensor
Networks

• By
• Seapahn Meguerdichian et. al.

Presented by Vijay Silva
2
Coverage

• What is coverage?
• Measure of the quality of service of a sensor
  network
• Coverage can be used to find weak/strong points
  in the sensor field, which could be used in
  future deployment schemes to improve quality of
  service
• Coverage viewpoints
• Worst Case Coverage Attempts to find areas of
  lower observability from sensors, and detect
  breach regions
• Best Case Coverage Attempts to find areas of
  high observability from sensors, and detecting
  regions of best support

3
Goals

• Contribute an optimal polynomial time algorithm
  for coverage in sensor networks
• Make use of existing computational geometric
  techniques and constructs, along with Graph
  theory techniques to develop a coverage algorithm.

4
Related Work

• The Art Gallery Problem
• Number of observers necessary to cover the art
  gallery room such that every point is seen by at
  least one observer
• Global Ocean Color
• Uses satellite data to observe oceanic
  phytoplankton
• Radar and Sonar coverage
• Attempts to optimally locate radars to achieve
  satisfactory coverage
• Coverage studies to maintain connectivity
• Optimum number of base stations required

5
Background

• Sensor Model
• Sensing ability is directly dependant on distance
• Sensor Location Technology
• Coverage not possible without location
  information
• Beacons A few sensor nodes that already know
  their location
• Predict location using RF signal strength
  information
• Requires a minimum of 3 beacon neighbors
  (trilateration)
• In reasonably dense networks, initially requires
  only 1 of nodes as beacons

6
Computational Geometry

• Voronoi Diagrams
• Partitions a plane containing a set of discrete
  sites into a set of convex polygons
• All points inside a polygon are closest to only
  one site
• Example

7
Computational Geometry (cont.)

• Delaunay Triangulation
• Directly related to the Voronoi diagram
• Connects the sites in the Voronoi diagram whose
  polygons share a common edge
• Ensures that sites that are close together are
  connected

8
Implementation

• Energy constraints
• Energy equation for communication between two
  arbitrary nodes
• E B . dy
• d distance between the two nodes
• y path loss exponent ( gt 1 )
• B proportionality constant describing the
  overhead per bit
• Using several intermediate hops is more efficient
  than using one longer hop
• Use compression to reduce the amount of network
  traffic
• Need to ensure that minimal amount of
  communication is required.
• Require location information for ALL nodes to
  compute the correct coverage solution

9
Coverage Types

• Coverage can be deterministic or stochastic
• Deterministic coverage A static network is
  deployed according to a predefined shape
• Sensor deployment styles
• Uniform, (e.g. a grid)
• Weighted
• Stochastic Coverage Sensors are randomly
  distributed in the environment

10
Worse Case Coverage

• Maximal Breach Path Given a sensor field in
  which each sensor location is known, need to
  identify the path between two given points with
  lowest observability
• Need to ensure that for any point on this path,
  the distance to the closest sensor is maximized
• Use the Voronoi diagram, since the line segments
  in the Voronoi diagram maximize the distance from
  the closest sites.

11
Maximal Breach Path

• How the algorithm works
• Generate the Voronoi Diagram for the sensor field
• Apply Graph theory abstraction
• Find the maximal breach path using Binary-Search
  and Breadth-First-Search
• The Voronoi diagram must be clipped along the
  boundaries

12
Maximal Breach Path (cont.)

• When converting the Voronoi diagram into a
  weighted, undirected graph
• Create a node for each vertex in the Voronoi
  diagram
• Create an edge for each line segment in the
  Voronoi diagram, assign the edge with its minimal
  distance from the closest sensor as its weight
• Perform a binary search between the smallest and
  largest edge weights in the graph

13
Maximal Breach Path (cont.)

• During each step of the Binary Search, check to
  see if a path exists using only edges with
  weights larger than the specified search criteria
  (breach_weight)
• If a path exists
• Increase breach_weight, and repeat the search
• If no path exists
• Reduce breach_weight to consider edges with lower
  weights

14
Maximal Breach Path (cont.)

• The maximal breach path is not unique
• Every edge in the breach path will have a weight
  larger than or equal to the breach_weight found
  by the algorithm, and at least one edge will have
  a weight equal to the breach_weight

15
Best Case Coverage

• Maximal Support Path Given a sensor field in
  which each sensor location is known, need to
  identify the path between two given points with
  the highest observability
• Need to ensure that for any point on this path,
  the distance to the closest sensor is minimized
• Use the Delaunay Triangulation, since the
  triangles produced will have minimum edge
  lengths.

16
Maximal Support Path

• The algorithm used is exactly the same as for
  Maximal breach path, with the following changes
• The Voronoi diagram is replaced by Delaunay
  Triangulation
• The edges in the graph are assigned weights equal
  to the length of the corresponding line segments
  in the Delaunay Triangulation
• The search parameter breach_weight is replaced
  with the parameter support_weight
• Support_weight is now an upper bound on all the
  edge weights that lie on the maximal support
  path, and there must exist at least one edge with
  weight equal to support weight

17
Algorithm Complexity

• Generation of Voronoi Diagram O(n log n)
• Graph conversion Linear time
• BFS search O(n) for sparse networks, and O(n2)
  in the worst case
• Binary Search O(log range)
• Algorithm Complexity O(n log n) (for sparse
  networks), or O(n2 log n) in the worst case.

18
Experimental Results

• The coverage algorithms were implemented and used
  in simulations
• The paths for a simulation of 30 sensors randomly
  deployed

19
Sample Results

• The Voronoi Diagram and Delaunay Triangulation
  for the previous sensor field.

20
Sensor Deployment Heuristics

• Deploying sensors along the Maximal Breach Path
  will improve overall coverage

21
Sensor Deployment Heuristics

• Deploying sensors at the midpoints of the edges
  in the maximal support path will further improve
  support coverage

22
Asymptotic Behavior

• The following graph shows the path results after
  random deployment of 100 sensors in a unit square
  field
• Certain levels of coverage can be expected even
  if the sensor deployment is random, given that a
  sufficient number of sensors are deployed

23
Future Research

• Algorithm assumes a centralized control server,
  need to consider strategies that make use of a
  more distributed control
• Consider different sensor models
• Non-isotropic sensor models, non-homogenous
  sensors

24
Critique

• The paths only consider edges where all edge
  weights are maximum/minimum
• Definition of maximal support path / maximal
  breach path not very clear.