Hole Detection in Sensor Network

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Hole Detection in Sensor Network
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What is a hole?

• Definition of hole
• Given a set of sensors and a target area, no
  coverage hole exists in the target area, if every
  point in the target area is covered by at least k
  sensors, where k is the required degree of
  coverage for a particular application.
• Reasons for hole
• Random deployment
• Sensor failures
• Location changes

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Distributed Coordinate-Free Hole Detection
Recovery

• Xiaoyun Li, David K. Hunter
• Univ. of Essex, UK

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Goal, Features and Assumptions

• Goal tell whether a sensor node is on the
  boundary of a hole, finally tell existence of
  holes.
• Features coordinate-free and distributed.
• Assumptions
• Each node has same sensing range R
• Covered two nodes are no more than R away
• Connected two nodes are no more than 2R away
  (link between them called Rc)

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Definition of a hole

• Hole in this paper--A single overlay coverage
  hole
• If (1) the target area can be partitioned into
  triangles formed by link Rc, (2) and no uncovered
  position exists inside each triangle, then no
  single overlay coverage hole exists in the target
  area.

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Definition of a hole (Contd)

• (1) the target area can be partitioned into
  triangles formed by link Rc,
• (2) and no uncovered position exists inside each
  triangle.

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Problem statement

• The problem is divided into two cases
• Large hole detection Check whether the target
  area can be partitioned into triangles by link
  Rc.
• Trivial hole detection If any uncovered position
  exists inside a triangle formed by link Rc, a
  trivial hole exists.

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Examples
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Criteria to discovery hole

• If graph G(V,E) can form a closed ring which
  cannot be partitioned into triangles, this ring
  is called a 3MeSH coverage ring.
• If the area bounded by the ring is also
  partitioned into triangles by links between node
  A and its connected neighbors, then node A is
  non-boundary node. Otherwise node A is a boundary
  node of a coverage hole.

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3MeSH coverage ring

• All the connected neighbors of node A can form a
  closed ring which cannot be partitioned into
  triangles.

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Node A is a non-boundary node.

• Neighbors of node A form a 3MeSH.
• Node A partitions the 3MeSH into triangles.

A
Node A
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Node A is a non-boundary node.

• Neighbors of node A form a 3MeSH.
• Node A partitions the 3MeSH into triangles.
• The two conditions cannot guarantee that A is a
  non-boundary node. Here is an exception.

A
The two conditions are satisfied, but A is still
a boundary node.
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Node A is a boundary node.

• Neighbors of A cannot form a 3MeSH
• Cannot form a ring.
• Or the ring can be partitioned into triangles.
• A cannot partition the 3MeSH into triangles.

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Hole detection procedure

• Elect a set V of active nodes
• Each active node determines whether it is a
  boundary node or non-boundary one.
• Detect holes among all the boundary nodes.
• Recovery the hole bounded by detected boundary
  node.

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How to elect active node

• Not all nodes need to be selected in graph.
• The selected ones are called active nodes rest
  ones are called redundant nodes.
• Each node can elect itself as the active node.
• Any node covered by an active node becomes a
  redundant node.
• All the uncovered nodes will elect themselves as
  active nodes.
• Those nodes having more links to adjacent active
  nodes have higher priority to become active.

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Three Conditions to determine a boundary node

• Nodes A and B are boundary nodes if they are
  connected, and there are fewer than two connected
  neighbors common to both A and B.
• Node A is a boundary node if the links between
  all its neighbors can partition the area into
  triangles. (By 3MeSH Definition)
• Node A is a boundary node if A has the same
  common neighbor set to other two neighbor nodes.
• Lack of proof that the three conditions are
  sufficient conditions.

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Large hole detection

• Each node collects connectivity information about
  its 1-hop and 2-hop neighbors.
• Therefore a hole enclosed by a polygon with at
  most 10 edges can be detected without any shorter
  path existing.

A B Path within 4 hops can be found
?? If each node can collect connectivity
information about its N-hop neighbors, then a
hole enclosed by a polygon with 4N2 edges at
most can be detected.
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Large hole recovery

• Similarly, if a redundant node is connected to
  all boundary nodes circulating a hole, all the
  boundary nodes form a 3MeSH coverage ring, so the
  hole is recovered.
• Find one redundant node connected to all the
  boundary nodes of a hole.
• If such redundant one doest exist, find a group
  of redundant nodes connected to all the boundary
  nodes of the hole.
• Carry out hole detection and boundary node
  detection inside the group. (Recursive)