, Volume 15, Issue 5, pp 495–519 | Cite as

Optimizing area for three-layer knock-knee channel routing

  • R. Kuchem
  • D. Wagner
  • F. Wagner


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.

Key words

VLSI-design Efficient algorithms Channel-routing Knock-knee mode Layer assignment 


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Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • R. Kuchem
    • 1
  • D. Wagner
    • 2
  • F. Wagner
    • 3
  1. 1.Institut für Geometrie und praktische MathematikRWTH AachenAachenGermany
  2. 2.Fakultät für Mathematik, Fachgruppe InformatikUniversität KonstanzKonstanzGermany
  3. 3.Institut für Informatik, Fachbereich MathematikFreie Universität BerlinBerlinGermany

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