  In the light of energy conservation and the expansion of existing networks,
wireless networks face the challenge of nodes with heterogeneous transmission
power. However, for more realistic models of wireless communication only few
algorithmic results are known. In this paper we consider nodes with arbitrary,
possibly variable, transmission power in the so-called physical or SINR model.
Our first result is a bound on the probabilistic interference from all
simultaneously transmitting nodes on receivers. This result implies that
current local broadcasting algorithms can be generalized to the case of
non-uniform transmission power with minor changes. The algorithms run in
$\O(\Gamma^{2} \Delta \log n)$ time slots if the maximal degree $\Delta$ is
known, and $\O((\Delta + \log n)\Gamma^{2} \log n)$ otherwise, where $\Gamma$
is the ratio between the maximal and the minimal transmission range. The broad
applicability of our result on bounding the interference is further
highlighted, by generalizing a distributed coloring algorithm to this setting.
