1. Dynamic Coverage In Wireless Ed-Hoc Sensor Networks
Academic Advisor: Dr. Michael Segal
Submitted by: Ilan Nitzani
Ron Porter

2. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Introduction
Personal computer and communication networks are constantly evolving.
Improvements in technology allow new sensing, storage, processing, and communication capabilities to be embedded into our daily lives
Networks are combined with the wireless ad hoc networking technology to facilitate inter-sensor communication.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

3. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Introduction (cont.)
Until now, sensor networks were mostly considered to be static.
But the topology of these networks can change over time:
A sensor with low power will have a fading transmission range.
Sensors may be turned off and on (for power saving).
Sensors may be inserted or extracted from the network, in accordance with demand.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

4. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Problem Definition
Two parameters help define the Quality Of Service that can be provided by a particular dynamic sensor network.
Best coverage radius.
Worst coverage radius.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

5. Problem Definition (cont.)
Best Case Coverage – the minimum coverage radius so that there exists a trajectory between 2 set points, that is completely covered by the sensor network.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

6. Problem Definition (cont.)
Worst Case Coverage – the maximum coverage radius so that there exists a trajectory between 2 set points, that is completely uncovered by the sensor network. (like a thief…)
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

7. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Best Case Solution
Regarding radius r we define as the region covered by all sensing disks of radius r.
We define a graph :
Sensors are vertices.
An edge exists between two vertices, if and only if the corresponding disks intersect.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

8. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Best Case Solution
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

9. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Best Case Solution
The problem is now a graph connectivity problem between the vertexes corresponding to points S and T.
Radius r must be big enough so that sensor nearest S will have S within it’s sensing disk (and similarly for T).
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

10. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Best Case Solution
We will consider the group of when .
Using a binary search we find the first i where S and T are connected in
This gives us an approximation of the solution.( ).
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

11. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Worst Case Solution
For Worst case, regarding radius r we define as the complement of region .
For given points S and T, we need to determine whether the region in containing S is connected to that containing T.
To simplify the problem each disk is represented by a square on the plane.
This is allowed since there is only a difference between 2-norm and infinity norm.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

12. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Worst Case Solution
In addition, we will represent regions in by their boundaries.
Only one of these regions can be infinite in area - the outer face. All other bounded regions will be called inner faces.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

13. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Worst Case Solution
When the outer cycle in (1) breaks into two cycles, it can either break into outer and an inner cycle (2), or it can break into two outer cycles (3).
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

14. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Worst Case Solution
Now we represent the outer cycles and the inner cycles by graph.
We can create a graph where the edges are the line segments and the vertices are the end points of the lines.
This will be our connectivity graph G( ).
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

15. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Worst Case Solution
To know whether a cycle is an inner cycle or an outer cycle, we need to identify the topmost edge of the cycle:
If the topmost edge of a cycle is a top boundary of a square then the cycle is an outer cycle.
If the topmost edge of a cycle is the bottom boundary of a square then the cycle is an inner cycle.
We need to maintain the topmost edge of each cycle as sensors move.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

16. Dynamic Coverage In Wireless Ad Hoc Sensor Networks
Worst Case Solution
The connectivity of G( ) is analogous to the connectivity of
Regions in are connected if and only if their boundary cycles are connected in the graph (and are actually the same boundary).
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

17. Implementation Example
Example for best coverage radius.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

18. Conclusion and Future Work
The best case implementation works best with over 5 sensors. Less than that cause the best case coverage radius to be more affected by the distance of the sensors from S or T, rather than the coverage factor the algorithm checks.
For multiplication factor we used More than that caused big jumps in sensing radius – which caused overlapping. A smaller multiplication factor slowed the program as it increased complexity.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks

19. Conclusion and Future Work
Future work on the subject includes implementation for worst case coverage radius, and using both implementations to perform statistical analysis of different sensor networks.
Dynamic Coverage In Wireless Ad Hoc Sensor Networks