Abstract
We discuss a new minimum density objective for spanning and Steiner tree constructions. This formulation is motivated by the minimum-area layout objective, which is best achieved through balancing the usage of horizontal and vertical routing resources. We present two efficient heuristics for constructing low-density spanning trees and prove that their outputs are on average within small constants of optimal with respect to both tree cost and density. Our proof techniques suggest a non-uniform lower bound schema which can afford tighter estimates of solution quality for a given problem instance. Furthermore, the minimum density objective can be transparently combined with a number of previous interconnection objectives (e.g., minimizing tree radius or skew) without affecting solution quality with respect to these previous metrics. Extensive simulation results suggest that applications to VLSI global routing are promising.