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 |
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 |
s adjacent grid points in A