1. Minimum Average Routing Path Clustering Problem in Multi-hop 2-D Underwater Sensor Networks Presented By Donghyun Kim Data Communication and Data Management Laboratory University of Texas at Dallas DIMACS/DyDAn Workshop: Approximation Algorithms in Wireless Ad Hoc and Sensor Networks DIMACS Center - Rutgers April 22 - 24, 2009

2. Agenda Introduction Preliminaries Minimum Average Routing Path Clustering Problem (MARPCP) - approximation scheme Faster 30 - approximation scheme Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

3. Underwater Sensor Networks (USNs) Applications ◦Oceanographic data collection ◦Pollution monitoring ◦Offshore exploration ◦Disaster prevention ◦Assisted navigation ◦Tactical surveillance Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

4. Underwater Sensor Networks (USNs) – cont’ Variable number of sensors and vehicles ◦Static sensors for traditional data collection ◦Unmanned Underwater Vehicles (UUV) ◦Deployed to perform collaborative monitoring tasks over a given area Connecting underwater instruments by means of wireless links based on acoustic communication Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

5. Underwater Sinks Multiple underwater sinks for relaying data to onshore or surface stations Involve in a lot of data transmission Spend more energy to transmit data to offshore or surface sinks Expensive Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

6. Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

7. Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

8. Agenda Introduction Preliminaries Minimum Average Routing Path Clustering Problem (MARPCP) - approximation scheme Faster 30 - approximation scheme Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

9. Routing Schemes in Wireless Networks Direct routing ◦Simple ◦Not cost and energy efficient Multi-hop routing ◦Evade energy exhausting long range direct communication ◦Increases the complexity of the routing ◦In multi-hop routing, the energy consumption for transmitting a message increases as the number of hops grows Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

10. Clustering for USNs USNs have decent mobility In dynamic wireless networks, clustering ensures basic level system performance (i.e. throughput and delay) Multi-level hierarchies for scalable ad-hoc routing (E.M. Belding-Royer, Wireless Networks, 2003) Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

11. Clustering-based Routing in Wireless Networks UW-Sinks Normal Nodes Clusterheads Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

12. Clustering-based Routing in Wireless Networks – cont’ UW-Sinks Normal Nodes Clusterheads Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

13. Data Fusion in Wireless Sensor Networks Normal Nodes Clusterheads It is around 10-12 Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

14. Agenda Introduction Preliminaries Minimum Average Routing Path Clustering Problem (MARPCP) - approximation scheme Faster 30 - approximation scheme Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

15. GOAL Finding an energy efficient clustering scheme for USNs using clustering-based routing scheme and limited data fusion (or requiring some level of data precision). Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

16. 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 Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

17. Problem Formulation d s The number of hops in total routing path Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

18. Problem Formulation – cont’ Minimum Average Routing Path Clustering Problem (MARPCP) ◦Given a set of sensor nodes and UW-Sinks on the Euclidean plane, MARPCP is find a set of clusterheads such that each sensor node is adjacent to at least one clusterhead, and the average distances from each clusterhead to its nearest UW-Sink is minimized. In other words, we want to minimize Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

19. A relaxation from MARPCP to Minimum Weight Dominating Set Problem (MWDSP) 3 2 1 1 1 1 1 3 2 3 2 3 4 1 Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

20. Agenda Introduction Preliminaries Minimum Average Routing Path Clustering Problem (MARPCP) - approximation scheme Faster 30 - approximation scheme Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

21. Algorithm 1 Lemma 1 ◦For any clusterhead and a UW-Wink,. Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

22. Algorithm 1 – cont’ Corollary 1 ◦Let A and B be a MARPCP and its corresponding (relaxed) MWDSP instances, respectively. Denote the cost function of feasible solutions for MARPCP and MWDSP by and, respectively. Then, for any feasible solution,. Proof of Corollary 1 ◦By Lemma 1, for every, Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

23. Algorithm 1 – cont’ Theorem 1 ◦A -approximation algorithm for MWDSP is a 3 -approximation algorithm for MARPCP. Proof 1 ◦ Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS UW-Sinks Normal Nodes Clusterheads

24. 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 April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

25. A Faster Heuristic Algorithm for MARPCP with A Constant Performance Ratio Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas 2 DIMACS

26. Agenda Introduction Preliminaries Minimum Average Routing Path Clustering Problem (MARPCP) - approximation scheme Faster 30 - approximation scheme Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

27. Algorithm 2 Analysis Lemma 2 ◦Let is an MIS included in of a node. Then,. Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

28. : all node in Level in tree Algorithm 2 Analysis – cont’ Theorem 2 ◦Algorithm 2 is a 30-approximation algorithm for MARPCP. Proof of Theorem 2 Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

29. Algorithm 2 Analysis – cont’ ◦Consider ◦All nodes in is dominated by ◦Let be the subset of dominated by. Then, ◦As is dominated by, from lemma 2, we have Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

30. Algorithm 2 Analysis – cont’ ◦By Algorithm 1, each must lie in either level of its corresponding shortest path tree. Thus, since. If follows that ◦Summing up for and we obtain Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS

31. Future Work Design a quick approximation algorithm ◦Ratio should be better than 30. Design a generalized distributed approximation algorithm ◦Support trade-off between data accuracy and energy-efficiency How to cluster USNs to deal with the unique properties and challenges How to incorporate an energy model? Presented by Donghyun Kim on April 22, 2009 Data Communication and Data Management Laboratory at The University of Texas at Dallas DIMACS