Distributed Algorithms for Dynamic Coverage in Sensor Networks

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Distributed Algorithms for Dynamic Coverage in
Sensor Networks

• Lan Lin and Hyunyoung Lee
• Department of Computer Science
• University of Denver

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Outline

• Dynamic maintenance of best and worst coverage
  radii
• Dynamic coverage with migration of redundant
  nodes
• Lazy coverage with different radii and limited
  mobility

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Best and Worst Coverage Radii

• Let D(P, r) be the union of all disks centered at
  points of P with radius r, where P is a set of
  sensor nodes.
• Best coverage radius is the minimum coverage
  radius r such that there exists a trajectory
  between S and T that is totally covered by D(P,
  r).
• Worst coverage radius is the maximum coverage
  radius r such that there exists a trajectory
  between S and T that is covered by the complement
  of D(P, r).
• Property
• For best (worst) coverage radius, there exists at
  least one pair of nodes whose disks are tangent
  to each other.

T
S
S
T
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Dynamic Maintenance of Best and Worst Coverage
Radii

• Given two sets of nodes P and Q, find the
  shortest distance
• D(P, Q) minp?P minq?Q d(p,q).
• Condition communication range is twice of
  sensing range.
• Scheme
• Maintain the coverage boundary.
• Detect a breach.
• Determine the new best and worst coverage radii.

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Maintenance of Boundaries

• Three types of boundary
• inner, outer, holes.
• Boundary events
• Loss of boundary node.
• Loss of non-boundary node.
• Non-boundary node moving within range of boundary
  nodes.
• Critical node
• Boundary node whose disk is not continuously
  covered by other nodes.

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Dynamic Best Coverage Radius

• Message complexity O (n1/2 log n).

T
S
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Dynamic Coverage with Redundant Nodes

• Redundant node node whose sensing disk is
  completely covered by other nodes.
• Redundant node as recovery node.
• Communication tree connect a non-redundant node
  to its closest recovery node.

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Tree Operations

• Insertion Non-redundant node and redundant node.

d
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b
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Deletion Redundant node.
a
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Dynamic Coverage Maintenance

• Energy costs
• Movement Em k d, where k is a constant
  determined by the vehicle,
  d is the distance moved.
• Sensing Es l r2, where l is a constant
  specified by the sensing equipment,
  r is the sensing radius.
• Total Etotal Em Es
• Suppose a failed node X has m neighbors, S1, S2,
  . . . , Sm. Let the area covered by each node be
  A(S i), for i 1, 2,. . .m. Let the area covered
  by X be A(X). Find the combination of movements
  of the neighbors to new positions P1, P2, . . . ,
  Pm and employments of different radii of sensing
  range for S1, S2, . . . , Sm, such that the
  following conditions are fulfilled.
• A(X) n (Ui A(S i)) is maximized,
• ?i Etotal, i is minimized.
• Lazy coverage strategy
• Each node knows its one- and two-hop neighbors.
• No recovery until a certain percentage of
  coverage loss occurs in one-hop neighborhood.

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Different Radii without or with Mobility