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Approximation Algorithm for Maximum Lifetime in Wireless Sensor Networks with Data Aggregation

Approximation Algorithm for Maximum Lifetime in Wireless Sensor Networks with Data Aggregation. Jeffrey Stanford and Sutep Tongngam. Presented by Gruia Calinescu. Outline. Network Model Contribution and related work Centralized algorithm Conclusions and future work. Network Model.

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Approximation Algorithm for Maximum Lifetime in Wireless Sensor Networks with Data Aggregation

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  1. Approximation Algorithm for Maximum Lifetime in Wireless Sensor Networks with Data Aggregation Jeffrey Stanford and Sutep Tongngam Presented by Gruia Calinescu

  2. Outline • Network Model • Contribution and related work • Centralized algorithm • Conclusions and future work

  3. Network Model • Sensor is on all the times • Sensor’s location is known • Adjustable communication range • Stationary • Report to Base station directly or via other sensors as relays • Data aggregation capability

  4. Contribution and related work • Contribution • Centralized algorithm with approximation ratio • Related work

  5. Base Base Base Base s2 s1 s3 s2 s2 s2 s1 s1 s3 s1 s3 s3 Centralized algorithm • Maximize Total time until the first sensor runs out of energy

  6. Problem formulation • Lifetime Maximization problem – To find a monitoring schedule {(Ar1,t1),…,(Ark,tk)} • Max  tAr • s.t. PAr (vi) tAr  E(vi) • PAr (vi) = TX(vi,vj=parent of vi in Ar)+(#children of vi in Ar)RX • Exact algorithm called MLDA (K.Kalpakis, K.Dasgupta, and P.Namjoshi) • O(n15logn)

  7. Base Ar1t1 s2 s1 s3 Base Ar2t2 Ar3t3 Base Base s2 s3 s1 s2 s2 s3 s1 s1 s3 Example schedule

  8. Approximation algorithms • Heuristics (K.Kalpakis, K.Dasgupta, and P.Namjoshi ) • G-CMLDA • I-CMLDA • Garg-Könemann approx. alg. with minimum length columns • Find Ar that Minimizes PAr (vi) yi • Minimum cost spanning arborescence problem

  9. Problem reduction Base Station r y2TX2,r PAr(s1) = y1TX1,2 s1 y2RX+y3TX3,2 y2RX + y1TX1,2 s2 s3 PAr(s2) = y2 (2RX +TX2,r ) PAr(s3) = y3TX3,2

  10. Approximation ratio • (1-ε) Garg-Könemann approx. alg. • Exact algorithm of finding minimum cost spanning arborescence • (1-ε) approximation ratio • O(n3 1/ε logn) complexity

  11. Experimental information • 40, 50, and 60 nodes in 50x50m2 • Base station is at (25,150) • Initial energy is 1 J. • Receiving power consumption • 50nJ/bit • Transmitting power consumption • 50 nJ/bit + 100*d2 pJ/bit • Package size 1000 bits

  12. Experimental result ε = 0.1

  13. Conclusion Centralized algorithm with (1- ε) approximation ratio Actual results on average within 2.5% of optimum Running time on average within 7% of one for finding optimum Future work Implement faster minimum cost arborescence algorithm Methods, tools for finding optimum of large sensor networks CPLEX on 80 nodes takes 28.5 hours Conclusions and Future work

  14. Questions? Thank You

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