1. Coverage and Connectivity in Sensor Networks
-Santosh Kumar

2. Model
Node distribution – Grid, Poisson, 2-D Gaussian (centered at grid points), etc.
Node Failure Probability – Nodes fail with some probability p for 0<= p < 1.
Sensing Range - A node can sense events in a disc of radius R.
Transmission Range – A node can communicate with another node if the distance between them is less than r.

3. Coverage
Full coverage – Every point in the area should be covered by some active node.
K-coverage - Every point in the area should be covered by at least K active nodes.

4. Problem
What conditions should be satisfied (relation between the number of nodes, sensing radius, and probability of failure of a node) to achieve full-coverage (K-coverage)?
Asymptotic Coverage – Pr (Full coverage) -> 1 as n -> infinity
Necessary and Sufficient conditions

5. Algorithmic Coverage
Once the physical network is K-covered, you can run distributed algorithms to prune the network to maintain K-coverage while allowing redundant nodes to sleep.
Objective – Minimize Power Consumption.
Sometimes, different degrees of coverage is needed for different applications.

6. Connectivity
Problem – Every active node should be connected to other active nodes.
K-connectivity – There exist at least K node disjoint paths between every pair of active nodes.
Motivation: load distribution, tolerance to failures.
Asymptotic Connectivity – Pr (network connected) -> 1 as n -> infinity

7. Relation between Coverage and Connectivity
Coverage does not imply connectivity r = R.
However, coverage implies connectivity if the r >= 2*R (Sensys 2003)

8. Approaches Percolation Theory Random Geometric Graph
Other approaches for Grid-based Model

9. Link Characteristics
Rayleigh Fading Model for node communication across one-hop
Link quality varies with distance
Link quality for the same distance is variable
Link quality for the same pair of nodes varies with time

10. Traffic Model Event to Sink Detection of an intruder
Locality of Event Detection - Several nodes in the vicinity of an intruder detect the same event.
Everyone sends the information to a sink
The number of packets routed to a node increases as one approaches closer to the base station.
Sometimes a tree is formed to route the event packets.