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A faster algorithm for rubber-band equivalent transformation for planar VLSI layouts

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2 Author(s)
H. -F. S. Chen ; Dept. of Electr. Eng. & Comput. Sci., Northwestern Univ., Evanston, IL, USA ; D. T. Lee

In this paper we consider the problem of transforming a single-layer topological routing of n two-terminal nets into a rubber-band equivalent using rectilinear wires in the presence of rectilinear circuit modules. Given a topological planar VLSI layout sketch with |F| features and |W| noncrossing wire segments connecting n two-terminal nets, we present an O(|F|·|W|) time algorithm to do the vertex-disjoint rubber-band equivalent transformation of these n nets if it exists. The algorithm consists of two phases, computing a loose homotopy with four spokes matrices, and computing a vertex-disjoint rubber-band equivalent of the given homotopy, each phase taking O(|F|·|W|) time and space. Both complexities are asymptotically optimal in the worst case. From the vertex-disjoint rubber-band equivalent of the given homotopy, one can obtain the detailed routing within the same time complexity. Experimental results are also presented

Published in:

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  (Volume:15 ,  Issue: 2 )