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VLSI Design
Volume 2 (1994), Issue 2, Pages 157-169

On the Minimum Density Interconnection Tree Problem

1cs Dept., University of California at Los Angeles, Los Angeles 90024-1596, CA, USA
2CS Dept., University of Virginia, Charlottesville 22903-2442, VA, USA
3EECS Dept., Northwestern University, 60208-3118, IL, USA

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.