Abstract
In this paper, we consider the problem of computing the map of geometric minimal cuts (MGMC) induced by a general planar embedding (i.e., the edge orientation is either rectilinear or diagonal) of a subgraph H = (V H , E H ) of an input graph G = (V,E). The MGMC problem is motivated by the critical area extraction problem in VLSI layout and finds applications in several other areas. In this paper, we extend an earlier result for planar rectilinear embedding to its more general case. The increased freedom on edge orientation in the embedding imposes new challenges, mainly due to the fact that the inducing region of a geometric minimal cut is no longer unique. We show that the MGMC problem can be solved by computing the L ∞ Hausdorff Voronoi diagram of a set of rectangle families, each containing an infinite number of axis-aligned rectangles. By exploiting the geometric properties of these rectangle families, we present an output-sensitive algorithm for computing the Hausdorff Voronoi diagram in this general case which runs in O((N + K) log2N loglogN) time, where K is the complexity of the Hausdorff Voronoi diagram and N is the number of geometric minimal cuts.
The research of the third author was supported in part by NSF under grant IIS-1115220.
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References
Abellanas, M., Hernandez, G., Klein, R., Neumann-Lara, V., Urrutia, J.: A Combinatorial Property of Convex Sets. Discrete & Computational Geometry 17, 307–318 (1997)
Dey, S.K., Papadopoulou, E.: The L ∞ (L1) Farthest Line-Segment Voronoi diagram. In: The Ninth International Symposium on Voronoi Diagrams in Science and Engineering, pp. 49–55 (2012)
Fortune, S.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2, 153–174 (1987)
Papadopoulou, E.: Critical area computation for missing material defects in VLSI circuits. IEEE Transactions on Computer-Aided Design 20(5), 583–597 (2001)
Papadopoulou, E.: Higher order Voronoi diagrams of segments for VLSI critical area extraction. In: The Eighteenth International Symposium on Algorithms and Computation, pp. 716–727 (2007)
Papadopoulou, E.: Net-aware critical area extraction for opens in VLSI circuits via high-order Voronoi diagram. IEEE Transactions on Computer-Aided Design 20(5), 583–597 (2011)
Xu, J., Xu, L., Papadopoulou, E.: Computing the Map of Geometric Minimal Cuts. In: The Twentieth International Symposium on Algorithms and Computation, pp. 244–254 (2009)
Xu, J., Xu, L., Papadopoulou, E.: Map of Geometric Minimal Cuts with Applications. In: Handbook of Combinatorial Optimization, 2nd edn. Springer (2013)
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Xu, L., Papadopoulou, E., Xu, J. (2013). Map of Geometric Minimal Cuts for General Planar Embedding. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_21
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DOI: https://doi.org/10.1007/978-3-319-03780-6_21
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