Energy Efficient Collaborative and Distributed Computatio n in Mesh-like Sensor Arrays

Sensor networks find use in a wide range of applications that i nvolve distributed and collaborative computations. Extensive research has focused upon design of ti me optimal parallel and distributed algorithms for two dimensional mesh connected computers (MCC). We show t at a large set of parallel algorithms (see Property 4.1), that take time T (n) and perform workW (n) on MCC of sizen, can be implemented on a wireless sensor mesh of size n in timeO(r2 + T (n=r2):r2) and energyO((n +W (n=r2):r2):rh). Here,r represents the transmission range and rh represents the transmission energy of a sensor. The algorithms are analyzed using two communication cost model s. We assumeh = 0 for the uniform cost model, andh = 2 for the square cost model. As a corollary of our result, we obt ain energy and time bounds of algorithms for summing, rank estimation and sorti ng, and show them to be energy optimal. The energy complexity for summing and rank estimation is given b y O(n:rh). Energy dissipation for sorting isO(npn:rh 1) for r < pn, andO(Min (n log n:rh; n:rh + npn:rh 1)) for r pn.

[1]  Deborah Estrin,et al.  GPS-less low-cost outdoor localization for very small devices , 2000, IEEE Wirel. Commun..

[2]  George Karypis,et al.  Introduction to Parallel Computing , 1994 .

[3]  Hongwei Zhang,et al.  GS3: scalable self-configuration and self-healing in wireless networks , 2002, PODC '02.

[4]  Deborah Estrin,et al.  Time synchronization for wireless sensor networks , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.

[5]  Mitali Singh,et al.  System-Level Energy Tradeoffs for Collaborative Computation in Wireless Networks , 2002 .

[6]  Stephan Olariu,et al.  Energy-efficient initialization protocols for radio networks with no collision detection , 2000, Proceedings 2000 International Conference on Parallel Processing.

[7]  S. Sitharama Iyengar,et al.  Introduction to parallel algorithms , 1998, Wiley series on parallel and distributed computing.

[8]  Hong Shen,et al.  Sorting on single-channel wireless sensor networks , 2002, Proceedings International Symposium on Parallel Architectures, Algorithms and Networks. I-SPAN'02.

[9]  Koji Nakano,et al.  Fundamental protocols for wireless sensor networks , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.

[10]  Russ Miller,et al.  Parallel algorithms for regular architectures - meshes and pyramids , 1996 .

[11]  Sartaj Sahni,et al.  Bitonic Sort on a Mesh-Connected Parallel Computer , 1979, IEEE Transactions on Computers.