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Coverage Problems in Wireless Adhoc Sensor Networks

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Title: 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.
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