Topological Hole Detection

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Topological Hole Detection

• Ritesh Maheshwari
• CSE 590

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Paper

• S. Funke, Topological Hole Detection and its
  Applications, DIALM-POMC, 2005.
• Basically, aim is to identify which nodes form
  the boundary, outer or inner (of holes), in a
  wireless sensor network

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Motivation

• Imagine a remote nature preserve
• Long summer drought, resulting in
• Wildfires!
• Airplanes dropping thousands of cheap sensor
  nodes, so that the sensor network
• Organizes itself, routes messages
• Identifies current firefront
• Answers Queries efficiently

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Motivation

• Imagine a remote nature preserve
• Long summer drought, resulting in
• Wildfires!
• Airplanes dropping thousands of cheap sensor
  nodes, so that the sensor network
• Organizes itself, routes messages
• Identifies current firefront gt Hole Detection!
• Answers Queries efficiently

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Other Uses

• Provide topology information to Location unaware
  protocols like GLIDER
• Help in Landmark selection for GLIDER
• Better Virtual coordinates in absence of Location
  Information

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Assumptions

• Region R
• Every point in R is covered for sensing by
  atleast one sensor
• Usually comm range larger than sensing range
• Unit Disk Graph
• No location information
• Only connectivity information available

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The continuous case

• A beacon point
• Construct contours of Euclidean distance from
  beacon
• Observation contours usually break at boundary

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Discrete Case

• No points only sensor nodes
• No distance measurement only hop-count
• Connected Components of same hop-count from
  beacon form contours

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Discrete Case

• Beacon node p
• dp(v) is hop-count from p to node v
• I(k) v dp(v) k is isoset of level k
• I(k) may be disconnected, so resulting connected
  components are called C1(k), C2(k), C3(k)..

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Discrete Case

• Boundary nodes are now the end nodes of the
  Connected Components - C1(k), C2(k) etc
• Pick random node r in Ci(k) and find nodes in
  Ci(k) with highest hop-count from r
• Usually, one beacon is not enough. They use 4

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Algorithms
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Beacon Selection

• The 4 beacons should be as far away as possible
• Choose 1st beacon randomly
• Other 3 chosen on the basis of their distance
  from the 1st beacon

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Distributed Implementation

• Topology exploration done only rarely
• Thus naïve implementation suits
• Can be done by Flooding a constant number of times

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Application Landmark Selection in GLIDER

• Landmarks divide the network into tiles using
  Voronoi diagrams
• Local coordinate system constructed within each
  tile
• When p in tilep wants to send packet to q in
  tileq,
• Inter-tile Packet is routed to a neighboring
  tile which is nearer to tileq than tilep and so
  on
• Intra-tile When reaching tileq, local coordinate
  system used to route to q

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Problems of unaware Landmark-Selection
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Problems of unaware Landmark-Selection
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Solution First Attempt

• Observation If 2 landmarks are on same hole
  boundary, then the hole cannot be totally inside
  one tile

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Solution Second Attempt

• Hole Repulsion and Pruning

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More Applications

• To find Virtual Coordinates in presence of holes
• Medial-Axis-Based Routing

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Evaluation UDG - random
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Evaluation UDG - grid
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Evaluation Non-UDG
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Conclusion

• Simple protocol
• Only Connectivity info required
• Hole detection gt Event detection
• But useful only for dense networks
• Not that bad, as they assume cheap sensors

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Thank You!

• ?