1. IEEE INFOCOM 2015
SURF: A Connectivity-based Space Filling Curve Construction Algorithm in High Genus 3D Surface WSNs
Chen Wang and Hongbo Jiang
Huazhong University of Science and Technology, China
{chenwang,
Hong Kong, April 29th, 2015

2. Performance Evaluation
Outline
Introduction
Preliminary
SURF Algorithm
Performance Evaluation
Conclusion

3. Performance Evaluation
Outline
Introduction
Preliminary
SURF Algorithm
Performance Evaluation
Ok, let’s get a starter. This talk lies in the session of SNs.
Conclusion

4. High Genus 3D Surface WSNs
1. And recently there have been increasing interests in scenarios ....
2. We can see that this kind of SNs is often of a complex-connected .... And thus it is modeled as ....
3. In our research, we focus on constructing ....
The three networks in (a-c) are homotopically equivalent to (d).

5. Space Filling Curve (SFC)
In mathematical analysis, the space filling curve refers to a curve whose range contains the entire 2D unit square (or more generally an N-D hypercube).
Almost all existing SFCs are constructed in squares or hyper-cubes.
These curves are recursively constructed.
All existing ....
In sensor networks, the sfc refers to a path ....

6. SFC Applications in WSNs
Serial Data Fusion [1, 2]
The query is successively (i.e., serially)
update from node to node until all nodes
in the network are visited. The last node
holds the right value of the query.
Path Planning of Mobile Nodes
Localization and coverage [3]
Sensor battery recharge [4]
Data collection by the data mules near the sink [5]
Linearization.
As far as we know, there are only two ....

7. SFC Construction in WSNs
X. Ban, M. Goswami, W. Zeng, X. Gu, and J. Gao, "Topology Dependent Space Filling Curves for Sensor Networks and Applications," in 32nd IEEE INFOCOM, 2013, pp
A. Mostefaoui, A. Boukerche, M. A. Merzoug, and M. Melkemi, "A Scalable Approach for Serial Data Fusion in Wireless Sensor Networks," Computer Networks, vol. 79, pp , 2015.
Both these algorithms are designed for 2D networks.
In our research, we propose ....

8. Directly connecting the iso-contours forms a SFC.
Our Approach
Intuition of SURF
It is noticed that the spherical surface ....
When it comes to ....
Iso-contours of a closed spherical surface naturally form an embryonic form of the SFC.
Directly connecting the iso-contours forms a SFC.

9. Our Approach Constructing SFCs in regions before connecting them.
Genus incurs two iso-contours.
Cutting off genus to form regions.
Obviously, it’s different ....
To tackle this issue, the main idea behind SURF is to ....
Constructing SFCs in regions before connecting them.

10. Performance Evaluation
Outline
Introduction
Preliminary
SURF Algorithm
Performance Evaluation
Conclusion

11. How can we know where the genus is?
Cut and Genus
A cut is referred to as a disjoint closed simple curve on a connected and orientable surface M.
The genus of M is defined as the maximum number of cuts without rendering M disconnected.
genus=1
genus=2
genus=3
As we want to cut the genus, ....
Here are some visual examples ....
Now we know the cut and the genus. The problem is how can we know ....
How can we know where the genus is?

12. Iso-contour and Reeb Graph
A iso-contour is a connected component of a level set, i.e. a curve whose points have a constant value.
The Reeb graph reveals the evolution of its level set.
Respecting to the ....
Given the reeb graph, now let’s see how to find the genus and the cut.

13. Cut Identification
Theorem 1. The Reeb graph of a closed orientable genus-n surface has exactly n loops [6].
An arc of the Reeb graph of M is a loop-end arc, if it is merged from two different arcs.
Corollary 2. Each loop in the Reeb graph of M corresponds to one loop-end arc.
We are motivated by the following theorem ....
So our method is to find a bisection ....

14. Performance Evaluation
Outline
Introduction
Preliminary
SURF Algorithm
Performance Evaluation
Conclusion

15. Proprocessing Triangulation of the Network [7]
The triangular structure is still denoted by M,
with its vertex (node) set V={vi} , and edge set
E = { e = (vi, vj) | vj is called the neighbor of vi }.
Given a triangular structure, our algorithm ....

16. Step 1: Contour Construction
Hop count distance → iso-distance contour.
Proposition 3: An iso-distance contour is a connected and closed cycle.
To construct the isocontours, ....
Now we can turn to cut id ....
We use a 4-step ....

17. Step 2: Cut Identification
(1) Assigning each node with an iso-contour ID. (2) Constructing regions (arcs). (3) Notifing loop-end regions (arcs). (4) Bisecting loop end regions.
By far we can get each genus a cut.

18. Step 3: Serial Traversal Scheme
The SFC construction follows several cases.
And now we can start ....

19. Performance Evaluation
Outline
Introduction
Preliminary
SURF Algorithm
Performance Evaluation
Conclusion

20. SURF is robust to general topologies.
Visual Results of SURF
We first examine ....
SURF is robust to general topologies.

21. SURF has a faster traversal speed.
Network Coverage
Next we evaluate the ....
The superiority of surf ....
SURF has a faster traversal speed.

22. Coverage v.s. Path Length
SURF guarantees a 100% coverage.

23. Performance Evaluation
Outline
Introduction
Preliminary
SURF Algorithm
Performance Evaluation
Conclusion

24. Conclusion
We proposed SURF, the first solution for the SFC construction in high genus 3D surface WSNs.
It requires connectivity information only, without the reliance on the location or distance measurement.
It does not rely on any particular communication model.
It is fully distributed and scalable, with a nearly constant storage and communication cost of every node.
A proportional coverage of the generated SFC, with an adaptive density for a given traversal budget or delay constrain will be an interesting direction for the future.

25. References
S. Patil, S. R. Das, and A. Nasipuri, "Serial Data Fusion Using Space-Filling Curves in Wireless Sensor Networks," in Proceedings of IEEE SECON, 2004, pp
A. Mostefaoui, A. Boukerche, M. A. Merzoug, et al., "A Scalable Approach for Serial Data Fusion in Wireless Sensor Networks," Computer Networks, vol. 79, pp ,
J. M. Bahi, A. Makhoul, and A. Mostefaoui, "Localization and Coverage for High Density Sensor Networks," Computer Communications, vol. 31, pp , 2008.
L. Xie, Y. Shi, Y. T. Hou, et al., "Making Sensor Networks Immortal: An Energy-Renewal Approach with Wireless Power Transfer," IEEE/ACM Transactions on Networking, vol. 20, pp , 2012.
R. Sugihara and R. K. Gupta, "Path Planning of Data Mules in Sensor Networks," ACM Transactions on Sensor Networks, vol. 8, pp. 1:1-1:27, 2011.
K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, et al., "Loops in Reeb Graphs of 2- Manifolds," in Proceedings of ACM SoCG, 2003, pp
H. Zhou, H. Wu, S. Xia, et al., "A Distributed Triangulation Algorithm for Wireless Sensor Networks on 2d and 3d Surface," in Proceedings of IEEE INFOCOM, 2011, pp
At last we provide ....

26. Thanks for your attentions !
IEEE INFOCOM 2015
Thanks for your attentions !
Networked and Communication Systems Research Group (NEST)