**On the Critical Transmission Range in
One-Dimensional**

**Sensor Networks Under Non-Uniform Node Placement
**

**Professor Armand M. Makowsk****i
**

We consider *n* sensors
independently placed at points X_{1},...,X* _{n}* on the
unit interval[0,1]according to some probability distribution
function F. Two sensor nodes communicate with each other if
their distance is less than some given transmission range

We assume that* **F*
admits a continuous density *f*,
and two qualitatively diﬀerent cases are identiŽed, namely *f* _{⋆}
> 0
and* **f*_{⋆}
= 0 with* **f*_{⋆}
= inf(*f*(*x*),*x* ∈
[0,1]). In each case, we present results on the form
of *ρ*^{*}_{n }and

*L*. In the process we make contact
with the existence and nature of critical thresholds for the property of graph
connectivity in the underlying geometric random graph. Engineering implications
for power allocation are discussed.

This is joint work with former Ph.D. student Guang Han (now at
Motorola).

**Wednesday, August 26, 2009**

**3-4 pm**

**Room 1200 EECS**