Sampling Based Sensor-Network Deployment

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Sampling Based Sensor-Network Deployment

• Volkan Isler, Sampath Kannan and Kostas
  Daniilidis
• University of Pennsylvania

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Outline

• Background knowledge
• Deployment Methods
• Conclusion
• Discussion

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Outline

• Background knowledge
• Deployment Methods
• Conclusion
• Discussion

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Deployment

• How to place sensor nodes in the target area
• In this paper, authors assumed it is impossible
  or very difficult to place sensors precisely (ex.
  Dissemination from airplane on foreign territory)
• Result in random geometric networks

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Deployment

• Two important requirements Coverage and
  Connectivity
• Coverage Every point in the environment is
  within the range of at least one sensor
• Connectivity Every sensor can communicate with
  every other sensor

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Deployment

• Problem What is the minimum number of sensors
  needed for guaranteed coverage and connectivity?
• Reasons why need minimum
• Too much cause interference, and easily detected
  by adversaries
• Decrease invasiveness in natural environment

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Two ways for deployment

• Deployment be accomplished in one step
• If deployment can implemented in multiple steps
  ? incremental deployment

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Sampling Based?

• The sample here is a term in machine learning
• Find most representative samples
• Sample Sensor units

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Critical Concepts

• Set-Systems
• Vapnik-Chervonenkis (VC) dimension

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Set System
EX X 1,2,3 R , 1, 2,
3, 1,2, 1,3, 2,3, 1,2,3
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VC-dimension

• a measure of the capacity of a statistical
  classification algorithm

VC-dimension
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VC-dimension
Find VC-dimension for disk set system
X all the points on the plane A the 3 black
points, is a subset of X
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VC-dimension
VC-dimension
Y is a subset of A (the 3 black points) R is the
certain subset of X such that R intersect A
become to Y (R is a certain collection of points
on the plane)
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VC-dimension
R
Find VC-dimension for disk set system
Y
Y is a subset of A (the 3 black points) R is the
certain subset of X such that R intersect A
become to Y (R is a certain collection of points
on the plane)
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VC-dimension
Find VC-dimension for disk set system
3 points shattered by 8 disks for any subset of
these 3 points, there exists a disk that contains
only those points and none other.
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VC-dimension
4 points can not be shattered There are no disks
that contain only the black points. So 3 is
VC-dimension of the disk set system
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Definition
Let sampling points form an . If
the size of event (R) is larger than specific
range (epsilon), the event will be intersected by
one of the sampling point.
If the sensors form an ,
this means any activity within a specified range
(determined by epsilon) will be intersected
(detected) by one of the sensors
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Outline

• Background knowledge
• Deployment Methods
• Conclusion
• Discussion

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One Step Deployment

• Find the necessary number of sensors to form
• By calculate
• - with this much points drawn at random from R
  is an epsilon-net with probability at least
• Place at location chosen uniformly

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One Step Deployment

• Make sure the connectivity
• Derive the lower bound communication range by

(random graph connectivity)
communication range
n n points sampled uniformly p graph is
connected with probability p
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Multiple Steps Deployment
Trivial but not ensure the connectivity
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SampleWithoutReplacement
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Multiple Steps Deployment
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SampleWithoutReplacdementwithComm
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Conclusion

• Guarantee coverage and connectivity using a few
  sensors as possible
• Model is general and simple, but can present
  bounds on the number of sensor required
• Two scenarios have been address concurrent and
  incremental deployment

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Discussion

• The target application for this paper is outdoor
  deployment, can we use these methods in indoor
  deployment?

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• Thank you!