  Contact graphs of isothetic rectangles unify many concepts from applications
including VLSI and architectural design, computational geometry, and GIS.
Minimizing the area of their corresponding {\em rectangular layouts} is a key
problem. We study the area-optimization problem and show that it is NP-hard to
find a minimum-area rectangular layout of a given contact graph. We present
O(n)-time algorithms that construct $O(n^2)$-area rectangular layouts for
general contact graphs and $O(n\log n)$-area rectangular layouts for trees.
(For trees, this is an $O(\log n)$-approximation algorithm.) We also present an
infinite family of graphs (rsp., trees) that require $\Omega(n^2)$ (rsp.,
$\Omega(n\log n)$) area.
  We derive these results by presenting a new characterization of graphs that
admit rectangular layouts using the related concept of {\em rectangular duals}.
A corollary to our results relates the class of graphs that admit rectangular
layouts to {\em rectangle of influence drawings}.
