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!