This paper presents a comprehensive state-of-the-art survey of the interconnection problem of large-scale circuits using design automation. The different types of routers in existence, as well as the implementation of some relevant algorithms are mentioned. The topological approach to layout design including applications of known results in Euclidean metric and some new results in rectilinear or Manhattan metric of topological invariants like thickness, are considered. The trend of future research and some of the important problems that demand attention, especially in the routing of multinets in multi-layers are cited. Attention is directed to the relatively new results as well as unreported results in progress, while the older results are adequately mentioned or referenced.
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