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, 2009 Mobile Computing and Wireless Networking Research Group at University of Texas at Dallas

Architecture for 2D underwater sensor networks (Image Source: http://www.ece.gatech.edu/research/labs/bwn/UWASN/figures/2D_arch.gif ) Presented by Donghyun Kim on February 19, 2009 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

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

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

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

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

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

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

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

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

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

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

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

Algorithm 1 – cont’ Theorem 1 Proof 1 A -approximation algorithm for MWDSP is a 3 -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

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

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

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

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

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

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