Title: power assignment problem in wireless networks.

Abstract.  Assigning power levels (corresponding to transmission ranges) to the
transceivers of a radio network, such that the total power consumption is as
low as possible, is often an extremely important issue.  Let $\P$ be a set of
$n$ points in the plane, representing $n$ transceivers.  We need to assign
transmission ranges to the transceivers in $\P$, so that (i) the resulting
communication graph is strongly connected; that is, the graph over $\P$ in
which there exists a directed edge from $p$ to $q$ if and only if $q$ lies
within the transmission range $r_p$ assigned to $p$, should contain a directed
path from any transceivers  $p \in \P$ to any other transceiver  $q \in \P$,
and (ii) the total power consumption (i.e., the cost of the assignment of
ranges) is minimized, where the total power consumption is a function of the
form  $\sum_{p \in \P} r_p^{\alpha}$, where $r_p$ is the range assigned to
transceiver $p$ and $\alpha > 0$ is a constant typically between 2 and 5.

The talk will be focus in three topics of the power assignment:
1. The case where only two power levels are available.
2. A new cost measure, namely, minimum area.
3. Finally, The power assignment with fault-tolerance problem.