  In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling
characterization of throughput scaling for random extended wireless networks
(i.e., $n$ nodes are placed uniformly at random in a square region of area
$n$). They showed that for small path-loss exponents $\alpha\in(2,3]$
cooperative communication is order optimal, and for large path-loss exponents
$\alpha > 3$ multi-hop communication is order optimal. However, their results
(both the communication scheme and the proof technique) are strongly dependent
on the regularity induced with high probability by the random node placement.
  In this paper, we consider the problem of characterizing the throughput
scaling in extended wireless networks with arbitrary node placement. As a main
result, we propose a more general novel cooperative communication scheme that
works for arbitrarily placed nodes. For small path-loss exponents $\alpha \in
(2,3]$, we show that our scheme is order optimal for all node placements, and
achieves exactly the same throughput scaling as in Ozgur et al. This shows that
the regularity of the node placement does not affect the scaling of the
achievable rates for $\alpha\in (2,3]$. The situation is, however, markedly
different for large path-loss exponents $\alpha >3$. We show that in this
regime the scaling of the achievable per-node rates depends crucially on the
regularity of the node placement. We then present a family of schemes that
smoothly "interpolate" between multi-hop and cooperative communication,
depending upon the level of regularity in the node placement. We establish
order optimality of these schemes under adversarial node placement for $\alpha
> 3$.
