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A Clustering Scheme for Energy- Efficient Routing in Multi-hop 2-D Underwater Sensor Networks

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A Clustering Scheme for Energy- Efficient Routing in Multi-hop 2-D Underwater Sensor Networks

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## A Clustering Scheme for Energy- Efficient Routing in Multi-hop 2-D Underwater Sensor Networks

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**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 KimFebruary 19, 2009Mobile 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, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**UW-Sinks**BackgroundsClustering in USNs Normal Nodes Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**UW-Sinks**Normal Nodes BackgroundsClustering in USNs – cont’ Clusterheads Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**It is around**10-12 Normal Nodes BackgroundsData Aggregation in Clustered USNs Clusterheads Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**UW-Sinks**Normal Nodes BackgroundsComm. Model in Related Work Clusterheads Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**Motivations**• 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) Motivations and Assumptions Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**UW-Sinks**Normal Nodes BackgroundsComm. Model in Our Work Clusterheads Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**d**The number of hops in total routing path s Problem Formulation Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**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 Problem Formulation – cont’ Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**3**4 1 2 3 3 1 2 2 1 1 3 1 A relaxation from MTRPCP to Minimum Weight Dominating Set Problem (MWDSP) 1 Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**Lemma 1**• For any clusterhead and a UW-Wink , . Algorithm 1 Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**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 , Algorithm 1 – cont’ Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**Theorem 1**• A -approximation algorithm for MWDSP is a 3 -approximation algorithm for MTRPCP. • Proof 1 Algorithm 1 – cont’ Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**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 Algorithm 1 – cont’ Presented by Donghyun Kim on February 19, 2009Mobile 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, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**Lemma 2**• Let is an MIS included in of a node . Then, . Algorithm 2 Analysis Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**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 Algorithm 2 Analysis – cont’ Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**Proof of Lemma 2 – cont’**• We know • Thus, since • In conclusion, Algorithm 2 Analysis – cont’ Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas**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) Future Work Presented by Donghyun Kim on February 19, 2009Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas