Barrier Coverage With Wireless Sensors

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Barrier Coverage With Wireless Sensors

• Santosh Kumar, Ten H. Lai, Anish Arora
• The Ohio State University

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Barrier Coverage
USA
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Belt or Belt Region
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Two special belt regions

• Rectangular
• Donut-shaped

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Crossing Paths

• A crossing path is a path that crosses the
  complete width of the region.

Crossing paths
Not crossing
paths
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K-Covered

• A crossing path is said to be k-covered if it
  intersects the sensing region of at least k
  distinct sensors.

3-covered
2-covered
0-covered
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K-Barrier Covered

• A belt region is k-barrier covered if all
  crossing paths are k-covered.

1-barrier covered
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Question 1

• Given a belt region deployed with sensors
• Is it k-barrier covered?

Is it 4-barrier covered?
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Is It k-barrier covered?

• Construct a coverage graph G(V, E)
• V sensor nodes, plus two dummy nodes L, R
• E edge (u,v) if their sensing disks overlap
• Region is k-barrier covered iff L and R are
  k-connected in G.

R
L
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Donut-shaped region

• Coverage graph G similarly constructed.
• k-barrier covered iff G has k essential cycles
  (that loop around the entire belt region).

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Is It k-barrier covered?

• Can be determined globally
• But not locally
• Localized algorithm is not possible
• In contrast, if a region is not k-blanket
  covered, it can be locally detected.

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Question 2

• Assuming sensors can be placed at desired
  locations
• What is the minimum number of sensors to achieve
  k-barrier coverage?
• k x l / (2r) sensors, deployed in k rows

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Question 3

• If sensors are deployed randomly
• How many sensors are needed to achieve k-barrier
  coverage with high probability (whp)?
• Desired are
• A sufficient condition to achieve barrier
  coverage whp
• A sufficient condition for non-barrier coverage
  whp
• Both conditions should converge asymptotically

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Conjecture critical condition for k-barrier
coverage

• If , then k-covered whp
• If , then not k-covered
  whp

s
1/s
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Weak and Strong Barrier Coverage

• A belt region B is said to be (strongly)
  k-barrier covered whp if
• A belt region is said to be weakly barrier
  covered whp if

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Weak Barrier Coverage

• Weak barrier-coverage whp
• A belt region is said to be weakly barrier
  covered whp if any set of congruent crossing
  paths is covered whp.
• Roughly speaking, we prove that
• If n sensors are deployed randomly in a unit area
  belt region where each sensors has a sensing
  radius of r, then
• In order to ensure weak k-barrier coverage whp,
  there must be at least log(n) active sensors in
  the r-neighborhood of each (shortest) crossing
  line.

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Determining Sensors to Deploy

• Given
• Length (l), Width (w), Sensing Range (r), and
  Coverage Degree (k),
• To determine sensors (n) to deploy, compute
• s2 l/w
• r(s) (r/w)(1/s),
• Compute the minimum value of n such that

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Summary of Contributions

1. Introduce the concept of barrier coverage
2. Show that testing barrier coverage locally is not
   possible, in general.
3. Propose an efficient (global) algorithm to
   determine if a given belt region is k-barrier
   covered with a sensor network.
4. Derive the optimal pattern of deployment to
   achieve k-barrier coverage when deploying
   deterministically.
5. Derive critical conditions for weak k-barrier
   coverage.