Minimum Density Interconnection Trees

We discuss a new minimum density objective for spanning and Steiner tree constructions in the plane. This formulation is motivated particularly by the need for balanced usage of routing resources to achieve minimum-area VLSI layouts. We present two efficient heuristics for constructing low-density spanning trees, and prove that their outputs are within small constants of optimal with respect to both tree weight and density. Our proof techniques suggest a non-uniform lower bound schema, which may be used to establish the quality of the heuristic solution for any given instance. More interesting is the fact that the minimum density objective can be transparently combined with a number of previous interconnection objectives, without affecting the solution quality with respect to these previous metrics. As examples, we show how sets of competing measures (e.g., cost, density, radius; or cost, density, skew) can be simultaneously optimized. Extensive simulation results suggest that applications to VLSI global routing are promising.
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Alpert, C, J Cong, A Kahng, G Robins, and M Sarrafzadeh. "Minimum Density Interconnection Trees." University of Virginia Dept. of Computer Science Tech Report (1992).