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Congestion estimation for 3D routing

Three-dimensional (3D) routing is an important step in deep sub-micron VLSI design. Given a 3D grid graph and a set of two-terminal nets to be routed, we propose a probabilistic model to calculate the routing density (congestion) on each edge of the grid graph. The routing density provides direct congestion estimation. Our experimental results demonstrate the effectiveness of the method on routing benchmarks.