Coverage Problems in Wireless Ad-hoc Sensor Networks

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Coverage Problems in Wireless Ad-hoc Sensor
Networks
Seapahn Meguerdichian, Farinaz Koushanfar,
Miodrag Potkonjak and Mani Srivastava INFOCOMM
- 2001
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Introduction

• Some issues arising in ad-hoc wireless sensor
  networks are
• location calculation, deployment, tracking and
  coverage
• Coverage Measure of the quality of service of a
  sensor network
• how well can network observe an area?
• Weak points can suggest future deployment or
  reconfiguration schemes
• what is the probability of an event being
  detected within a time frame?

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Problem definition

• Different viewpoints of coverage
• Worst-case coverage Quantify the QoS by finding
  areas of lower observability from sensor nodes
  and detecting breach regions
• Best Case Coverage Detect areas of high
  observability from sensors, and regions of best
  support
• Goal Given a sensor network deployment,
  efficiently find the maximal breach and
  supporting paths

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Sensing Model Assumptions

• Sensing ability is directly dependant on distance
• Sensor locations
• 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)
• Iterative trilateration
• In reasonably dense networks, initially requires
  only 1 of nodes as beacons
• Solutions requires locations of sensors

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Solutions

• Based on computation geometry ideas
• Voronoi diagram
• Delaunay Triangulation

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Voronoi Diagrams

• The Voronoi diagram of a set of points partitions
  the plane into convex polygons such that all
  points inside a polygon are closest to point
  inside the polygon

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Voronoi Diagram Construction

• Construct a bisector between one site and all
  others.
• A Voronoi cell is the intersection of all
  half-planes defined by the bisectors.

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Delaunay Triangulation

• Related to the Voronoi diagram (dual of each
  other)
• Connects the sites(points) in the Voronoi diagram
  whose polygons share a common edge
• Ensures that sites that are close together are
  connected

Voronoi Edge
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Worst Case Coverage

• Given Field A instrumented with sensors areas I
  and F.
• Problem Identify PB, the maximal breach path in
  S, starting in I and ending in F.
• PB is defined as a path with the property that
  for any point p on the path PB, the distance from
  p to the closest sensor is maximized.
• Intuition
• Find a path such that any point on path always is
  at least breach_width distance away
• Maximum value of breach_width leads to worst case
  coverage and minimizes observability along path

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Voronoi Diagram
By construction, each line-segment maximizes
distance from the nearest point
(sensor). Consequence Path of Maximal Breach
of Surveillance in the sensor field lies on the
Voronoi diagram lines
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Formulation

• Given Voronoi diagram D with vertex set V and
  line segment set L and sensors S
• Construct graph G(N,E)
• Each vertex vi?V corresponds to a node ni ?N
• Each line segment lii ?L corresponds to an edge
  ei ?E
• Each edge eii?E, Weight(ei) Distance of li
  from closest sensor sk?S
• Formulation Is there a path from I to F which
  uses no edge of weight less than K?

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Algorithm

• Generate Voronoi Diagram
• Apply Graph-Theoretic Abstraction (generate graph
  from diagram)
• Search for PB
• Check existence of path I --gt F using Breadth
  First Search and Binary Search
• Perform a binary search between the smallest and
  largest edge weights in the graph
• 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)
• PB is maximal breach path
• Every edge in the breach path has weight larger
  than or equal to the breach_weight, and at least
  one edge will have a weight equal to the
  breach_weight

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Best Case Coverage

• Given Field A instrumented with sensors areas I
  and F
• Problem Identify Ps, the maximal support path in
  S, starting in I and ending in F.
• Ps is defined as a path with the property that
  for any point p on the path Ps, the distance from
  p to the closest sensor is minimized.
• Intuition
• Find a path such that any point on path always is
  at most support_width distance away
• Minimum value of support_width leads to worst
  case coverage and maximizes observability along
  path

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Maximal Support Path
Use the Delaunay Triangulation Property Triangle
s formed have minimum edge lengths Ps has to
lie on these edges
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Algorithm

• The algorithm used is exactly the same as for
  Maximal breach path, with the following changes
• The Voronoi diagram is replaced by the Delaunay
  triangulation as the underlying geometric
  structure
• The edges in graph G are assigned weights equal
  to the length of the corresponding line segments
  in the Delaunay triangulation
• The search parameter breach_weight is replaced by
  the new 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

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Complexity

• Generation of Voronoi Diagram O(n log n)
• Graph conversion and weight assignment O(n)
• BFS search O(m),
• where m is the number of edges
• O(n) for sparse networks, and O(n2) in the worst
  case
• Binary Search O(log range)
• Total O(n log n) (for sparse networks), or
  
• O(n2 log n) in the worst case (??)

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Results
The paths for a simulation of 30 sensors randomly
deployed
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Results

• Voronoi Diagram and Delaunay Triangulation of the
  30 node network

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Maximal Breach Path Example (50 nodes)
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Maximal Breach Path Example (200 nodes)
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Deployment Heuristics
Adding sensor along breach and support weight
edges to improve breach coverage and support
coverage
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Asymptotic Behavior

• Average over 1000 random deployments of 100 nodes
• Support 1 support_weight
• Certain levels of coverage can be expected even
  if the sensor deployment is random, given that a
  sufficient number of sensors are deployed

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Conclusions

• Problem formulation to determine worst-case and
  best-case coverage as a QoS metric
• Used computation geometry constructs and
  properties
• Heuristics can help future deployments
• Using breach_weight and support_weight edges

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Comments

• Maximize support Minimize support_weight
• Change algorithm in Fig 2 to consider only
  weights less than support_weight for each
  iteration
• Other considerations
• Distributed solution
• Nodes are not location-aware
• Metrics of coverage (other than distance based)
• Multiple coverage (more-reliable)
• Duty-cycling (subset of nodes awake different at
  different times)
• End-to-end metric (current metric will place
  nodes only at breach_weight, support_weight
  edges)
• Speed of object movement