Topological Hole Detection
Ritesh Maheshwari
CSE 590
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
Motivation
Imagine a remote nature preserveLong summer drought, resulting inWildfires!Airplanes dropping thousands of cheap
sensor nodes, so that the sensor network: Organizes itself, routes messages Identifies current firefront Answers Queries efficiently
Motivation
Imagine a remote nature preserveLong summer drought, resulting inWildfires!Airplanes dropping thousands of cheap
sensor nodes, so that the sensor network Organizes itself, routes messages Identifies current firefront => Hole Detection! Answers Queries efficiently
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
Assumptions
Region REvery point in R is covered for sensing by
atleast one sensor Usually comm range larger than sensing range
Unit Disk GraphNo location informationOnly connectivity information available
The continuous case
A beacon pointConstruct contours of
Euclidean distance from beacon
Observation: contours usually break at boundary
Discrete Case
No ‘points’ – only sensor nodes
No ‘distance’ measurement – only hop-count
Connected Components of same hop-count from beacon form contours
Discrete Case
Beacon – node pdp(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)…..
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
Algorithms
Beacon Selection
The 4 beacons should be as far away as possible
Choose 1st beacon randomlyOther 3 chosen on the basis of their
distance from the 1st beacon
Distributed Implementation
Topology exploration done only rarely
Thus naïve implementation suits
Can be done by Flooding a constant number of times
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
Problems of unaware Landmark-Selection
Problems of unaware Landmark-Selection
Solution: First Attempt
Observation: If 2 landmarks are on same hole boundary, then the hole cannot be totally inside one tile
Solution: Second Attempt
Hole Repulsion and Pruning
More Applications
To find Virtual Coordinates in presence of holes
Medial-Axis-Based Routing
Evaluation: UDG - random
Evaluation: UDG - grid
Evaluation: Non-UDG
Conclusion
Simple protocolOnly Connectivity info requiredHole detection => Event detection
But useful only for dense networksNot that bad, as they assume cheap
sensors
Thank You!