  In this paper, we address the problem of broadcasting in a wireless network
under a novel communication model: the {\em swamping} communication model. In
this model, nodes communicate only with those nodes at geometric distance
greater than $s$ and at most $r$ from them. Communication between nearby nodes
under this model can be very time consuming, as the length of the path between
two nodes within distance $s$ is only bounded above by the diameter $D$, in
many cases. For the $n$-node lattice networks, we present algorithms of optimal
time complexity, respectively $O(n/r + r/(r-s))$ for the lattice line and
$O(\sqrt{n}/r + r/(r-s))$ for the two-dimensional lattice. We also consider
networks of unknown topology of diameter $D$ and of a parameter $g$ ({\em
granularity}). More specifically, we consider networks with $\gamma$ the
minimum distance between any two nodes and $g = 1/\gamma$. We present broadcast
algorithms for networks of nodes placed on the line and on the plane with
respective time complexities $O(D/l + g^2)$ and $O(Dg/l + g^4)$, where $l \in
\Theta(\max\{(1-s),\gamma\})$.
