Topological Hole Detection

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 • 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)…..

10. 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

11. Algorithms

12. 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

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 tilepwants to send packet to q in tileq, • Inter-tile: Packet is routed to a neighboring tile which is nearer to tileq than tilepand so on • Intra-tile: When reaching tileq, local coordinate system used to route to q

16. Problems of unaware Landmark-Selection

17. 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! 