3-dimensional Routing

Consider a single planar grid, or two parallel planar grids of size w × n. The vertices of the grids are called terminals and pairwise disjoint sets of terminals are called nets. We aim at routing all nets in a cubic grid (above the single grid, or between the two grids holding the terminals) in a vertex-disjoint way. However, to ensure solvability, it is allowed to extend the length and the width of the original grid to w = sw and n = sn by introducing s− 1 pieces of empty rows and columns between every two consecutive rows and columns containing the terminals. Hence the routing is to be realized in a cubic grid of size (s · n)× (s ·w)× h. The objective is to minimize the height h. The above problems are motivated by VLSI design, where technological improvements of the past two decades motivated the research of routing problems with a “real” 3-dimensional flavour. In this paper we survey a few recent results.