contact Rectangular Layouts and Contact Graphs

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