1. at University of Texas at Dallas
A Clustering Scheme for Energy- Efficient Routing in Multi-hop 2-D Underwater Sensor Networks
Donghyun Kim, Wei Wang, Ling Ding, Jihwan Lim, Weili Wu, and Heekuck Oh,
A Clustering Scheme for Energy-Efficient Routing in Multi-hop 2-D Underwater Sensor Networks, to appear in Optimization Letters.
Presented By Donghyun Kim February 19, Mobile Computing and Wireless Networking Research Group
at University of Texas at Dallas

2. Architecture for 2D underwater sensor networks
(Image Source: )
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

3. Backgrounds Clustering in USNs
UW-Sinks
Normal Nodes
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

4. Backgrounds Clustering in USNs – cont’
UW-Sinks
Normal Nodes
Clusterheads
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

5. Backgrounds Data Aggregation in Clustered USNs
It is around
10-12
Normal Nodes
Clusterheads
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

6. Backgrounds Comm. Model in Related Work
UW-Sinks
Normal Nodes
Clusterheads
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

7. Motivations and Assumptions
Energy is a scarce resource in USNs
Clustering makes USNs energy efficient
Energy consumption increases exponentially as the transmission range grows => Multi-hop transmission preferred
Total energy consumption is closely related to the number of hops over which a message travels
Assumptions
USNs are homogeneous
Each clusterhead is used as a local data aggregation point
Clustering-based shortest path routing is used as a routing scheme
Each sensor node sends a report message to the sink regularly (i.e. every hour)
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

8. Backgrounds Comm. Model in Our Work
UW-Sinks
Normal Nodes
Clusterheads
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

9. Problem Formulation d The number of hops in total routing path s
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

10. Problem Formulation – cont’
Minimum Total Routing Path Clustering Problem (MTRPCP)
Given a set of sensor nodes and UW-Sinks on the Euclidean plane, MTRPCP is find a set of clusterheads such that each sensor node is adjacent to at least one clusterhead, and the total distances from each clusterhead to its nearest UW- Sink is minimized. In other words, we want to minimize
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

11. A relaxation from MTRPCP to Minimum Weight Dominating Set Problem (MWDSP)3 4 1 2 3 3 1 2 2 1 1 3 1 1
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

12. Algorithm 1 Lemma 1 For any clusterhead and a UW-Wink , .
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

13. Algorithm 1 – cont’ Corollary 1 Proof of Corollary 1
Let A and B be a MTRPCP and its corresponding (relaxed) MWDSP instances, respectively. Denote the cost function of feasible solutions for MTRPCP and MWDSP by and , respectively. Then, for any feasible solution ,
Proof of Corollary 1
By Lemma 1, for every ,
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

14. Algorithm 1 – cont’ Theorem 1 Proof 1
A -approximation algorithm for MWDSP is a approximation algorithm for MTRPCP.
Proof 1
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

15. Algorithm 1 – cont’ Existing algorithms for MWDSP.
Slow algorithms (centralized, enumeration)
72-approximation = 216-app. for MTRPCP
-approximation = app. for MTRPCP
Quick Algorithm (distributed, greedy)
-approximation = app. For MTRPCP
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

16. A Faster Heuristic Algorithm for MTRPCP with A Constant Performance Ratio
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

17. Algorithm 2 Analysis Lemma 2
Let is an MIS included in of a node . Then,
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

18. Algorithm 2 Analysis – cont’
Theorem 2
Algorithm 2 is a 90-approximation algorithm for MTRPCP.
Proof of Theorem 2
: all node in Level
Consider and
All nodes in is dominated by
From lemma 2, we have
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

19. Algorithm 2 Analysis – cont’
Proof of Lemma 2 – cont’
We know
Thus,
since
In conclusion,
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

20. Future Work Design a quick approximation algorithm
Ratio should be better than 30.
Design a slow approximation algorithm
Ratio should be better than
We have => hopefully in next week
Design a generalized distributed approximation algorithm (d-hop case, in writing)
Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas