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Topological Via Minimization Revisited
November 1991 (vol. 40 no. 11)
pp. 1307-1312

The topological via minimization problem in a two-layer environment is considered. A set of n two-terminal nets in a bounded region is given. The authors attempt to find a homotopy to assign nets to distinct layers so that no two nets on the same layer cross each other and the number of vias is minimized. A recursive approach in which an optimal solution to a two-sided channel routing problem is used as a basis is used to solve this problem optimally. The notion of partition number K of a circle graph is introduced, and the total running time of the via minimization algorithm is shown to be O((n/K)/sup 2K-2/ log (n/K)), where n is the total number of nets.

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Index Terms:
topological via minimization problem; two-layer environment; two-terminal nets; bounded region; homotopy; optimal solution; two-sided channel routing problem; partition number; circle graph; circuit layout CAD; graph theory.
M. Sarrafzadeh, D.T. Lee, "Topological Via Minimization Revisited," IEEE Transactions on Computers, vol. 40, no. 11, pp. 1307-1312, Nov. 1991, doi:10.1109/12.102839
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