1. Topological Hole Detection Ritesh Maheshwari CSE 590

2. 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

3. 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

4. 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 => Hole Detection!  Answers Queries efficiently

5. 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

6. 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

7. The continuous case A beacon point Construct contours of Euclidean distance from beacon Observation: contours usually break at boundary

8. Discrete Case No ‘points’ – only sensor nodes No ‘distance’ measurement – only hop-count Connected Components of same hop-count from beacon form contours

9. Discrete Case Beacon – node p d p (v) is hop-count from p to node v I(k) = { v : d p (v) = k} is isoset of level k I(k) may be disconnected, so resulting connected components are called C 1 (k), C 2 (k), C 3 (k)…..

10. Discrete Case Boundary nodes are now the end nodes of the Connected Components - C 1 (k), C 2 (k) etc Pick random node r in C i (k) and find nodes in C i (k) with highest hop-count from r Usually, one beacon is not enough. They use 4

11. Algorithms

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

13. Distributed Implementation Topology exploration done only rarely Thus naïve implementation suits Can be done by Flooding a constant number of times

14. Application: Landmark Selection in GLIDER Landmarks divide the network into tiles using Voronoi diagrams Local coordinate system constructed within each tile When p in tile p wants to send packet to q in tile q,  Inter-tile: Packet is routed to a neighboring tile which is nearer to tile q than tile p and so on  Intra-tile: When reaching tile q, local coordinate system used to route to q

16. Problems of unaware Landmark-Selection

18. Solution: First Attempt Observation: If 2 landmarks are on same hole boundary, then the hole cannot be totally inside one tile

19. Solution: Second Attempt Hole Repulsion and Pruning

20. More Applications To find Virtual Coordinates in presence of holes Medial-Axis-Based Routing

21. Evaluation: UDG - random

22. Evaluation: UDG - grid

23. Evaluation: Non-UDG

24. Conclusion Simple protocol Only Connectivity info required Hole detection => Event detection But useful only for dense networks Not that bad, as they assume cheap sensors

25. Thank You!