1. Load Balanced Routing with Constant Stretch for Wireless Sensor Network with Holes
Good afternoon everyone.
My present today is about a load balanced routing with constant stretch for wireless sensor network with holes
Nguyen Phi Le, Nguyen Duc Trong and Nguyen Khanh Van
Ha Noi University of science and technology

2. Agenda Background Related works Problem statement and goals
Proposed scheme
Strategy to choose the forbidding area
Hole bypassing routing protocol
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

3. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

4. Background Geographic routing Uses location information of the nodes
Each node knows the location of the neighbors and the destination
Achieves near optimal path with network without holes

5. Background Geographic routing with holes Hole diffusion problem
As you know, geographic routing is a popular approach and used widely in sensor network as it is very simple and scalable.
For networks without of the holes, geographic routing can achieve a near optimal routing path.
But for networks with holes, geographic routing faces some critical problems.
One of that is the hole diffusion problem.
like this.
What you see in the slide is a network with a hole in the center.
When the source and the destination stay in two side of the hole, the packet tends to be routed along the node on the hole boundary like this.
Thus, the boundary nodes are imposed a more traffic than the others and the energy of these node will run out quickly and become dead nodes.
And then, the hole is enlarged like this.

6. Background Geographic routing with holes Hole diffusion problem
Routing path enlargement problem
Another problem is routing path enlargement.
As the nodes don’t know about the presence of the hole in advance and the packet is route a long the boundary of the hole.
The routing path tends to be enlarged.
For example,
As you can see in the slide, the red line is the routing path.
This path is longer than this optimal path.

7. Background Common approach
Constructing a forbidding area around the hole
Nodes know the hole in advance
Routing the packet along optimal path outside the forbidding area
So ,
To cope with these two problem of the geographic routing with hole, a common approach is to build a forbidding area around the hole,
Disseminate information of this forbidding area to the node in the network, so, they can know about the hole in advance.
When a source node which has knowledge of the hole want to send a packet, it can calculate the optimal path bypassing the forbidding area
And the packet is routed along this optimal path.

8. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

9. Related works Target the hole diffusion problem
Virtual hexagon [H.Choo, ICOIN’11]
Virtual Circle [F.Yu, JCN 2009]
The forbidding area is very simple
The dissemination cost is small
Virtual ellipse [Y.Tian, ICC’08]
There are several related works have been done on this area.
In the slide are three researches which target the problem of hole diffusion.
In these ones,
The author create a forbidding area with very simple shape, like a hexagon, a circle, a ellipse.
The pros of these approaches is the information describe the forbidding area is very simple and thus the cost to dissemination infromation of the forbidding area is small.
These approaches somehow solves the problem of hole diffusion but

10. Related works Hole diffusion problem has not been solved thoroughly
Static forbidding area
Traffic is concentrated around the forbidding area
Routing path is enlarged in some cases
It can not solve that problem thoroughly
Because, the forbidding area is static,
Thus, instead of the hole boundary, the traffic is imposed on the boundary of the forbidding area.
Another problem is that,
For some kind of network, the difference between the hole and the forbidding area is very large, and this difference cause the enlargment of the routing path as you can see in the slide

11. Data congestion on the boundary of the convex hull
Related works
Target the routing path enlargement problem S D
GOAL
[Transaction on parallel and distributed computing, 2011]
Visibility graph [G.Tan, infocom 2009]
Constant stretch
Here is another work, where author proposed a hole bypassing routing protocol with a constant stretch.
In this work, the convex hull of the hole is used as the forbidding area.
And the packet is routed along the vertices of the convex hull.
With this protocol, the routing path can achieved a constant stretch,
But, the data congestion is occurred on the boundary of the convex hull
Hole
BUT
Convex hull
Data congestion on the boundary of the convex hull

12. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

13. Problem statement
Hole diffusion problem has not been solved thoroughly
Static forbidding area
Traffic is concentrated around the forbidding area
None of the existing schemes solves both of the two problems
So,
As you can see,
The problem of the existing researches are that:
First, the hole diffusion problem has not been solvef throughly
And , non of the ….

14. Goal Finding the optimal forbidding area
Constant stretch
Load balancing
Small dissemination cost
Propose a hole bypassing routing scheme which
Has a constant stretch
Solves the problem of hole diffusion thoroughly
So,
We have two goals in this research.
First, as there are many shape like circle, ellipse, hexagon, convex hull has been chosen to be the forbidding area,
We want to find, what is the optimal forbidding area.
And then, using that optimal forbirding area, we proposa a hole ….

15. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

16. Theoretical model Considering networks with only one hole
Modeling the geographic S-D routing path as the Euclidean line between S and D
Real geographic routing path
Euclidean routing path
Firstly, we will describe our theoretical model.
In this research, we consider networks which contain only one hole
And we assume that, the network is dense of sensors everywhere apart from the considered hole,
Then with this assumption, we can model the shortest routing path from S to D as the shortest euclidean line between S and D.
For example,
This is the hole, the black line is the real routing path
, we approximate this routing path by the euclidean path, which is represented by this red line.

17. Theoretical model Euclidean stretch of the forbidding area to the hole
And, now is the definition of the euclidean stretch of a forbidding area to the hole.
Assume this is a hole, and it is covered by this forbidding area.
For this pair of S and D,
This is the shortest euclidean routing path bypassing the hole and this is the euclidean routing path which bypassed the forbidding area.
Then the stretch of the forbidding area to the hole is the ratio of the length of the euclidean path bypassing the forbidding area to the length of the shortest euclidean routing path bypassing the hole.
Hole
𝐸𝑢𝑐𝑙𝑖𝑑𝑒𝑎𝑛 𝑠𝑡𝑟𝑒𝑡𝑐ℎ= max ∀(𝑆,𝐷) 𝑆 𝐴 𝑖 …𝐴 𝑗 𝑆 𝐻 𝑙 … 𝐻 𝑘
Forbidding area
Shortest Euclidean routing path bypassing the hole
Euclidean routing path bypassing the forbidding area

18. Strategy to choose the forbidding area
Constant stretch
Load balancing
Small dissemination cost

19. Strategy to choose the forbidding area
The shortest Euclidean path bypassing a polygon
broken line through the vertices of the convex hull
Now we will see what is the optimal forbidding area.
Firstly, we will find what kind of the forbidding area can achieve the best routing path stretch.
We found that, for an arbitrary polygon, then the shortest euclidean path bypasing the polygon is the broken line through the vertices of the convex hull of that polygon.
Please look at the slide.
This is a polygon
And this is the convex hull of the polygon.
Then, for any pair of source and destination which stay on opposite sides of the polygon,
The shortest euclidean path from source and destination is the broken line which connect the source, destination, and the vertices of the convex hull.
Convex hull of polygon P:
a convex polygon which covers P and
its vertices are the vertices of P

20. Strategy to choose the forbidding area
The shortest Euclidean path bypassing a polygon
broken line through the vertices of the convex hull
Is the convex hull the best forbidding area ???
The Euclidean stretch of the convex hull to the hole is 1
Now we will see what is the optimal forbidding area.
Firstly, we will find what kind of the forbidding area can achieve the best routing path stretch.
We found that, for an arbitrary polygon, then the shortest euclidean path bypasing the polygon is the broken line through the vertices of the convex hull of that polygon.
Please look at the slide.
This is a polygon
And this is the convex hull of the polygon.
Then, for any pair of source and destination which stay on opposite sides of the polygon,
The shortest euclidean path from source and destination is the broken line which connect the source, destination, and the vertices of the convex hull.

21. Strategy to choose the forbidding area
The shortest Euclidean path bypassing a polygon
broken line through the vertices of the convex hull
The number of the vertices of the convex hull maybe very large
The dissemination cost is large too
The reason is that, the verties number of the convex hull maybe very large and dissemination the information of convex hull to the node in the network may consume a great network resource.

22. Strategy to choose the forbidding area
The forbidding area should be a convex polygon
Hole bypassing routing path
Although the convex hull is not the optimal forbidding area, it is clear that, the optimal forbidding area should be a convex polygon, not a concave polygon.
Like this
And the routing path which bypass the forbidding are should be the path along the broken line connecting
Hole
Forbidding area

23. Strategy to choose the forbidding area
If P is a n-gon with equal angles such that P covers the hole and each edge of P contains at least one vertex of the hole, then Euclidean stretch of P to the hole is upper bounded by 1 sin (𝑛−2)𝜋 2𝑛
We choose the octagon with the equal angles as the forbidding area
The Euclidean stretch does not exceed 1 sin 3𝜋 8
We found another fact that, …
Ok, so the conclusion is that:
The forbidding area should be an octagon with all angles is the same,
With this kind of forbidding area, we need only 8 vertices to represent it and we can assure that the E-stretch does not exceed ….

24. Strategy to choose the forbidding area
Constant stretch
Load balance
Small dissemination cost
Traffic concentration around the boundary of the forbidding area
Hole
Forbidding area

25. Strategy to choose the forbidding area
The Euclidean stretch depends on
Perimeter of the forbidding area
Distance between the source and the destination
The larger the distance, the smaller the Euclidean stretch
The Euclidean stretch does not depends on
The position of the forbidding area
Dynamic forbidding area
The size and the position are packet specific
Fortunately,
We found that,
The e-stretch of a forbidding area to the hole depends only on its perimeter and the distance of the source and the destination.
And, with the same forbiding area , the source-destination with further distance will achieve a smaller stretch.
So, we decide to chose a dynamic forbidding area, which has the size and the position specified by each packet.
Like this,
If the soure and destination near to each other, then they will use a small forbidding area,
And if the source and destination far from each other, they will use a big forbidding area

26. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

27. Proposed protocol detail
Initial network setup
Hole bypassing protocol
Now, I will describe our routing protocol in detail
Our protocol consists of two phases: initial network setup and routing protocol

28. Proposed protocol detail
Initial network setup
Identifying hole boundary
Determining core polygon
Disseminating information of core polygon to a restricted area
Hole bypassing protocol
1. Identifying hole boundary
2. Determining core polygon
3. Disseminating core polygon
4. Hole bypassing protocol

29. Initial network setup Core polygon construction
Here is the way to construc the core polygon.
Firstly, we construct
1. Construct a rectangle circumscribing the hole
2. Construct another rectangle circumscribing the hole with edge directions of angle of 3𝜋 4 to the first

30. Initial network setup Core polygon construction
3. The intersections of the two rectangles form the core polygon

31. Initial network setup Core polygon information dissemination
Region 1
Region 2
Dissemination area is restricted by predefined threshold δ
𝑃 𝐶 𝑙(𝑁) 𝛽(𝑁) 𝛽(𝑁) ≤ 1 sin 3𝜋 8 +𝛿
pC: perimeter of the core polygon; l(N): distance from N to the core polygon ; β(N): view limit from N to the core polygon

32. Proposed protocol detail
Initial network setup
Identifying hole boundary
Determining core polygon
Disseminating information of core polygon to a restricted area
Hole bypassing protocol
1. Identifying hole boundary
2. Determining core polygon
3. Disseminating core polygon
4. Hole bypassing protocol

33. Hole bypassing protocol
The packet is initiated in region 2
Region 1
Region 2

34. Hole bypassing protocol
The packet is initiated in region 1 (or arrived at a node in region 1)
Region 1 I
Region 2
Determines the forbidding area (A-polygon): Image of the core polygon through a homothetic transformation
The center is chosen randomly
The scale factor 𝜉> 1 is computed based on source-destination distance

35. Hole bypassing protocol
The packet is initiated in region 1 (or arrived at a node in region 1)
Region 1 I
Region 2
Random selection of I ↓
Forbidding area is different per packet
Scale factor is computed based on the source-destination distance ↓
Constant stretch of routing path

36. Hole bypassing protocol
The packet is initiated in region 1 (or arrived at a node in region 1)
Region 1 I
Region 2
Determines shortest Euclidean path which bypasses the A-polygon
Virtual anchors: vertices of A-polygon
Routes the packet to the virtual anchors

37. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

38. Performance evaluation
Theoretical analysis
Proves the constant Euclidean stretch of the proposed protocol
Simulation
Compares performance with existing protocols

39. Theoretical analysis Constant stretch
Euclidean stretch does not exceed to 1 sin⁡( 3𝜋 8 ) +𝛿 (~1.09+δ）
( 𝛿: predefined parameter)
𝑆 𝐴 𝑖 …𝐴 𝑗 𝑆 𝐻 𝑙 … 𝐻 𝑘 < 1 sin⁡( 3𝜋 8 ) +𝛿

40. Simulation Benchmarks Evaluation metrics
Virtual Circle [F.Yu, transaction on communication and network ]
Virtual hexagon [H.Choo, ICOIN’11]
Convex hull [Transaction on parallel and distributed computing, ]
Evaluation metrics
Stretch in hop-count
The ratio between the hop-count of the routing path using routing protocol and the optimal routing path.
Energy consumption of individual sensor nodes
Energy overhead
The extra energy caused by the initial network setup phase in our protocol.

41. Simulation Simulation scenario Simulator :NS2
Network area: 1000m x 1000m
Sensor nodes: 1500
Number of the hole: 1
Number of the vertices of the hole: 52
Simulation time: 500s
Number of source-destination pair: 100 pairs
Packet transmission frequency: 1packet/1s
(Victor Shnayder et al., Simulating the power consumption of large scale
sensor network applications, SenSys’04 )

42. Simulation Simulation result Stretch
Smaller than “virtual hexagon”, “virtual circle”
Greater than “Goal” but the difference is not much
Less than 1.2 (with δ=1)
Does not increase when decreasing the distance between source- destination

43. Simulation Simulation result
Energy consumption of individual sensor nodes
“Goal” is the worst
The proposed scheme is the most balanced compared to the existing protocols
GOAL
Proposed scheme(𝛿=1)
Virtual hexagon
Virtual circle

44. Simulation Simulation result Energy overhead
Decreases with the increasing of the stretch
Just accounts for only 0.095% of the entire energy even in the worst case

45. Agenda Background Related works Problem statement and goals
Strategy to choose the forbidding area
Our proposed routing scheme
Performance evaluation
Conclusion and future work
This is the agenda.
Firstly, I introduce the background of our research and the related works,
And then, describe our routing protocol and evaluate the performance of it.
Finally, I conclude my presentation and introduce our future work

46. Conclusion and future work
We proposed a routing protocol to bypass the hole
Solves the problem of hole diffusion
Ensures a constant stretch
Euclidean stretch <1.09+𝛿 , theoretically
Proposed scheme outperforms existing protocols by simulation
Hop-count stretch <1.2 (with 𝛿=1)
Future work
Consider the network with multiple holes
Compare performance of our protocol with non-geographic routing protocols

47. Thank you for your attention !