Wireless Ad Hoc and Sensor Networks

CDS-based Distributed Data Collection

 269

r

−

α

since r is the maximum transmission range of a node (defined in Section 11.3).

Furthermore, if we abstract a data transmission link as a node as shown in Figure

11.1(a), then, for the nodes in S

R

, the densest packing of nodes is the hexagon pack-

ing [226] with edge length I as shown in Figure 11.1(b). Subsequently, the nodes in

S

R

can be layered with respect to v

i

(abstracted by the transmission link from s

i

to

s

j

), with the l-th layer having at most 6l nodes. Furthermore, the distance between v

i

and any node at the l-th layer is no less than

√

3

2

lI. Then, we have



s

k

∈S

R

,s

k

=s

i

D(s

k

,s

j

)

−

α

(11.9)

≤ 6 ·I

−

α

+



l≥2

6