The VLSI layout problem in various embedding models

  • Michael Formann
  • Frank Wagner
VLSI Layout
Part of the Lecture Notes in Computer Science book series (LNCS, volume 484)


In 1984 Kramer and van Leeuwen proved a fundamental complexity result of VLSI layout theory. They showed that the so-called General Layout Problem, i.e. the problem of embedding a graph into a grid of minimum area is NP-hard, even for connected (but not necessarily planar) graphs.

VLSI circuits (or large parts of them) are typically modelled by planar graphs, but Kramer and van Leeuwen used a family of non-planar graphs for their reduction and they posed the complexity of minimum area layouts of planar connected graphs as an open problem.

  • close a gap in their proof,

  • extend the NP-hardness result to the more realistic class of planar connected graphs and

  • show this for three different embedding models, including the Manhattan and the knock-knee model.


VLSI layout routing NP-completeness embedding models Manhattan model knock-knee model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Michael Formann
    • 1
  • Frank Wagner
    • 1
  1. 1.Institut für Informatik, Fachbereich MathematikFreie Universität BerlinBerlin 33

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