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• W2953153977 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 $O(nlog n)$-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., $Omega(nlog n)$) 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}." @default.
• W2953153977 created "2019-06-27" @default.
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• W2953153977 date "2006-11-21" @default.
• W2953153977 modified "2023-09-27" @default.
• W2953153977 title "Rectangular Layouts and Contact Graphs" @default.
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