The VLSI layout problem in various embedding models
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.
KeywordsVLSI layout routing NP-completeness embedding models Manhattan model knock-knee model
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