Abstract
In this paper we consider the channel-routing problem in the knock-knee mode. An algorithm is presented to construct a layout that is wirable in only three conducting layers. When the channel consists of top-to-bottom nets only, the layout is optimal with respect to the area. In case there are one-sided nets, the algorithm introduces at most one additional column. The algorithm improves all previously known layout algorithms which either use up toN/2 (N number of nets) additional columns to produce a three-layer wirable layout [6], [11], [12] or construct a layout which might not be three-layer wirable [4], [5], [10], [18]. Using a special kind of segment tree as the basic data structure, the algorithm can be implemented to run inO(N logN) time. Previous algorithms with linear running time use either additional columns [6], [12] or solve only special cases [18], [19]. For any layout constructed by the algorithm (or a slightly modified layout) a three-layer assignment can be constructed in timeO(N) with onlyO(N) vias.
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Communicated by T. Nishizeki.
A preliminary version of this paper was presented under the title “Area-Optimal Three-Layer Channel Routing”, at the 30th IEEE Symposium on Foundations of Computer Science, 1989. Part of this work was done while Dorothea Wagner and Frank Wagner were with Lehrstuhl für Angewandte Mathematik insbesondere Informatik, RWTH Aachen. Dorothea Wagner acknowledges the Deutsche Forschungsgemeinschaft for supporting this research in part under Grant Mö 446/1-1 and the Forschungsinitiativprojekt of the Technische Universität Berlin for supporting this research under Grant FIP 3/1. Frank Wagner acknowledges the Deutsche Forschungsgemeinschaft for supporting this research in part under Grant We 1265/1-1.
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Kuchem, R., Wagner, D. & Wagner, F. Optimizing area for three-layer knock-knee channel routing. Algorithmica 15, 495–519 (1996). https://doi.org/10.1007/BF01955047
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DOI: https://doi.org/10.1007/BF01955047