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In this paper we propose a general framework for viewing a class of heuristics for track assignment in channel routing from a purely graph theoretic angle. Within this framework we propose algorithms for computing roufing solutions using optimal or near optimal number of tracks for several well-known benchmark channels in the two-layer VH, three-layer HVH, and multi-layer Vi Hi and Vi Hi+l routing models. Within the same framework we also design an algorithm for minimizing the total wire length in the two-layer VH and three-layer H V H routing models.

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