On a solution of a randomized three tracks variant of the Gate Matrix Layout problem Original Research Article

We are concerned with the k-Gate Matrix Layout (k-GML) problem in a very large scale integration design. The problem asks if k tracks are enough to lay out a given circuit. The k-GML problem may be stated equivalently in terms of random Boolean matrices. In the paper, we find thresholds for the appearance of matrices which are ‘yes’ instances for a randomized 3-GML problem.