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Rectangular Layouts and Contact Graphs

Adam L. Buchsbaum·Emden R. Gansner·Cecilia M. Procopiuc·Suresh Venkatasubramanian
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Abstract

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 $Ω(n^2)$ (rsp., $Ω(n\log n)$) 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}.

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Adam L. Buchsbaum, Emden R. Gansner, Cecilia M. Procopiuc, Suresh Venkatasubramanian. 2006-11-21. Rectangular Layouts and Contact Graphs. https://arxiv.org/abs/cs/0611107

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