The full text of this article:

Topology control with Hexagonal Tessellation
by Ren Ping Liu, Glynn Rogers, Sihui Zhou, John Zic
International Journal of Sensor Networks (IJSNET), Vol. 2, No. 1/2, 2007
Abstract: Geographic Adaptive Fidelity (GAF) is an important topology control approach in Wireless Sensor Networks. It extends the system lifetime by exploiting node redundancy. However, the properties of the square grid in GAF have not been fully studied. This paper shows that there exists an unreachable corner in the GAF grid architecture. Using an analytical model, we are able to calculate the unreachable probability and analyse its impacts on data delivery. We propose to replace the square grid of GAF with Hexagonal Tessellation (GAF-h). We then proceed to prove that GAF-h is able to achieve zero loss with little extra cost when compared to the original scheme. A node association algorithm is also proposed for efficient implementation. This algorithm is proved to integrate with the original GAF protocol with little computing overhead.

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