Coverage and Connectivity of Sensor Networks

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Coverage and Connectivityof Sensor Networks
Prof. Yu-Chee Tseng CSIE/NCTU
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Outline

• Coverage, Connectivity, and Object Discovery
• Coverage and Connectivity Problems
• Object Discovery 802.11 vs. Bluetooth

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Introduction

• Wireless sensor networks
• Wireless communication technologies
• Embedded micro-sensing MEMS technologies
• Each sensor is capable of
• Collecting, storing, and processing environmental
  information
• Communicating with neighboring nodes

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Sensors

• MICA MOTE (Berkeley)

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Coverage Problems

• In general
• Determine how well the sensing field is monitored
  or tracked by sensors.
• Possible Approaches
• Geometric Problems
• Surveillance and Exposure
• Area Coverage
• Coverage
• Coverage and Connectivity
• Coverage-Preserving and Energy-Conserving Problem

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Review Art Gallery Problem

• Place the minimum number of cameras such that
  every point in the art gallery is monitored by at
  least one camera.

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Review Circle Covering Problem

• Given a fixed number of identical circles, the
  goal is to minimize the radius of circles.

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Surveillance and Exposure

• Breach and support paths
• paths on which the distance from any point to the
  closest sensor is maximized and minimized
• Voronoi diagram and Delaunay triangulation
• Exposure paths
• Consider the duration that an object is monitored
  by sensors

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Coverage and Connectivity

• A region is k-covered, then the sensor network is
  k-connected if RC ? 2RS
• Extending the coverage such that connectivity is
  maintained.

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Coverage-Preserving and Energy-Conserving
Protocols

• Sensors' on-duty time should be properly
  scheduled to conserve energy.
• thus extending the lifetime of the network.
• This can be done if some nodes share the common
  sensing region.

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The Coverage Problem in a 2D Space
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k-Coverage Problem

• Given a set of sensors deployed in an area, is
  every point in the area is covered by at least k
  sensors?
• k is an integer
• This is a decision problem!
• Applications
• positioning
• location tracking
• fault tolerance

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An Example
Is this area 1-covered?
In fact, this area is not only 1-covered but also
2-covered.
Whats the level of coverage of this area?
Is this area 5-covered?
1-covered means each location is within at least
one sensor's sensing range.
2-covered means each location is within at least
two sensor's sensing range.
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Version 1k-Unit-Disk Coverage Problem

• The sensing distances of all sensors are the
  same.
• I.e., r1 r2 rn.

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Version 2k-Non-Unit-Disc Coverage Problem

• The sensing distance of each sensor may be
  different.

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Assumptions

• Each sensor is aware of its geographic location
  and sensing radius.
• Each sensor can communicate with its neighbors.
• Difficulties
• O(n2) regions may be divided by n circles.
• It is very difficult to determine these regions.

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The Proposed Solution

• We try to look at how the perimeter of each
  sensors sensing range is covered.
• How a perimeter is covered implies how an area is
  covered
• by the continuity of coverage of a region
• By collecting perimeter coverage of each sensor,
  the level of coverage of an area can be
  determined.
• a distributed solution

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How to Calculate the Perimeter Coverage of a
Sensor?
Si is 2-perimeter-covered
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Relationship between k-covered and
k-perimeter-covered

• THEOREM 1. Suppose that no two sensors are
  located in the same location. The whole network
  area A is k-covered iff each sensor in the
  network is k-perimeter-covered.

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Detailed k-UC/k-NC Algorithm

• Each sensor independently calculates its
  perimeter-covered.
• k mineach sensors perimeter coverage
• Time complexity ndlog(d)
• n number of sensors
• d number of neighbors of a sensor

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Simulation Results
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A Toolkit
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Summary

• Two new coverage problems
• k-UC and k-NC.
• We have proposed efficient polynomial-time
  solutions.
• Simulation results and a toolkit based on
  proposed solutions are presented.

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The Coverage Problem in a 3D Space
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The 3D Coverage Problem

• Definition
• Given a set of sensors deployed in a
  three-dimensional cuboid sensing field A, is
  every point in A is covered by at least k
  sensors?
• The sensing region of each sensor is modeled by a
  3D ball
• The proposed solution
• We reduce the decision problem from a 3D space to
  one in a 2D space, and then to one in a 1D space.

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Details of the proposed solution

• To determine whether the whole network is
  sufficiently covered
• Look at the sphere of a sensor
• To determined whether each sensor's sphere is
  sufficiently covered,
• Look at the circle of each spherical cap of a
  sensor intersected by its neighboring sensors is
  covered.
• By collecting this information from all sensors,
  a correct answer can be obtained.

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A Spherical Cap
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Theoretical Fundamentals

• 3D gt 2D
• THEOREM 2. If each sphere is k-sphere-covered,
  then the sensing field A is k-covered.
• 2D gt 1D
• COROLLARY 1. Consider any sensor si. If each
  point on Si is k-cap-covered, then sphere Si is
  k-sphere-covered.
• THEOREM 3. Consider any sensor si and each of its
  neighboring sensors sj. If each circle Cir(i,j)
  is k-circle-covered, then the sphere Si is
  k-cap-covered.

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The Relationship between Two Caps Case 1

• The center of Cap(i,k), Cen(i, k), is inside
  Cap(i,j)

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The Relationship between Two Caps Case 2

• The center of Cap(i,k), Cen(i, k), is outside
  Cap(i,j)

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How to calculate the circle coverage of a circle?

• Similar to what we do in the 2D problem.

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Complete Algorithm

• Each sensor independently calculates circle
  coverage of each of its spherical cap on its
  sphere.
• A sensors sphere coverage
• min circle coverage
• Collect this information from each sensor.
• The coverage level of the whole network min
  sphere coverage
• Complexity
• Calculate a sensors sphere cover O(d2logd)
• Overall O(nd2logd)

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Summary

• Newly define the coverage problem in a 3D space.
• Solution
• 3D gt 2D gt 1D
• Network coverage gt sphere coverage gt circle
  coverage

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Applications of Coverage

• Discovering Insufficiently Covered Regions
• Power Saving
• Covering Hot Spots
• Irregular Sensing Regions

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Discovering Insufficiently Covered Regions

• Theorem 1 provides a necessary and sufficient
  condition to determine if an area in the network
  is k-covered.
• Each sensor determines which segments of its
  perimeter are less than k-perimeter-covered.
• By putting all segments together, we can
  precisely determine which areas are less than
  k-covered.

BACK
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Applications Power Saving

• On the contrary, a sensor network may be overly
  covered by too many sensors in certainly areas.
• If there are more sensors than necessary, we may
  turn off some redundant nodes to save energy.

BACK
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Covering Hot Spots
BACK
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Irregular Sensing Regions
BACK
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Coverage-Preserving and Energy-Saving Issue
Basic Idea

• The time axis is divided into rounds with equal
  duration.
• Each sensor node generates a reference time in
  each round.
• Intersection points between sensors' sensing
  ranges are used to evaluate whether the area is
  sufficiently covered or not
• Each sensor has to join the schedule of each
  intersection point within the sensor's sensing
  range.

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An Example

Round 1
Round 2
Round n
Sensing phase
Initial phase
Initial phase