We present approximations to non-smooth continuous functions by differentiable functions which are parameterized by a scalar beta>0 and have convenient limit behavior as beta -> 0. For standard numerical methods, this translates into a tradeoff between solution quality and speed. We show the utility of our approximations for wirelength and delay estimations used by analytical placers for VLSI layout. Our approximations lead to more "solvable" problems.
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