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The Computer Journal 1994 37(5):449-462; doi:10.1093/comjnl/37.5.449
© 1994 by British Computer Society
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An Efficient Polynomial-Time Algorithm for Three-track Gate Matrix Layout

N. G. Kinnersley * and W. M. Kinnersley *

Department of Computer Science, University of Kansas, Lawrence, KS 66045-2192, USA

Gate Matrix Layout (GML) is a combinatorial optimization problem that arises in several VLSI layout styles. It is known to be equivalent to other important problems in combinatorial graph theory including vertex separation and pathwidth. While the general problem is N P-complete, when the relevant parameter is fixed, the decision problem can be solved in polynomial time. While solutions with time-complexities O(n) and O(n2) are known, all of those presented so far are impractical due to the presence of extremely large coefficients. Herein we present an efficient O(n3) algorithm for the three-track GML decision problem. The approach we use lays out connected subgraphs in each step thereby constructing a solution when one exists. The algorithm has performed efficiently when used on graphs with over 200 edges.

Received November, 1993. revised February, 1994.

* Department of Computer Science, University of Kansas, Lawrence, KS 66045-2192, USA


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