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Table 1 List of notations introduced in this paper

From: Geographical model-derived grid-based directional routing for massively dense WSNs

Notation Description
\(\mathcal {C} (x,y)\) Tansmission cost for nodes at (x,y)
P Minimum cost (geodesic) path between two positions
ρ(x,y) Amount of information generated at (x,y)
D(x,y) Routing vector field, the direction points to the next forwarding node and |D(x,y)| represents the amount of information transmitted at (x,y)
A, ∂A ROI, boundary of ROI
|v| Length of a vector v
u f Unit vector pointing to the next forwarding node
ψ Node density distribution
r Distance between wireless sender and receiver
α rf Radio frequency (RF) attenuation exponent
Grid point at the ith row and the jth column
Set of grid points in A
T(x,y) Minimum routing cost from nodes at (x,y) to sinks
\(\tilde {f}_{{i},{j}}\) Value of function or vector f (e.g., T or D) at
Set of s adjacent grid points in A
E(x,y) Initial energy at (x,y)
e(x,y) Transmission energy consumption per unit of information at (x,y)
λ(x,y) e/E, normalized transmission energy cost per unit of information at (x,y)
\(\mathcal {J}\) 1/λ 2
Φ Potential of D
\(\hat {\mathbf {n}}\) Unit inward pointing normal vector to ∂A