An efficient layer assignment algorithm for gridless switchbox routing

Abstract

A graph-theoretic algorithm is presented for the layer assignment and via minimization of a gridless switchbox routing. A concept called via propagation is used to facilitate the minimization of vias. The time complexity of the proposed algorithm is O( <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</e1> log <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</e1> + <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K </e1> ), where <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</e1> is the number of routing wire segments in the layout and <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</e1> is the maximum number of vias that can occur. The approach achieves the minimum number of vias for several difficult switchbox problems