A unified approach to partitioning and placement (VLSI layout)

Using a geometrical model and a matrix inner product technique, it is demonstrated that partitioning and placement are mathematically equivalent. Depending on whether the cost measure is based on Manhattan or Euclidean square distance, either a linear programming or a quadratic programming approach can be applied for solutions of both problems. Two general algorithms based on quadratic programming are discussed in detail. The first algorithm is based on eigenvector decomposition, applicable for designs in which all modules are movable. The eigenvector approach gradually reduces the search space and hence reaches the global optimum in an effective way. The second approach, based on solving linear equations, is very efficient in terms of memory usage and run time and gives excellent results for two-way partitioning. It is especially useful for high-complexity circuit layout that has some input/output pads fixed around the chip boundary, since it takes care of the inherent sparsity. An efficient algorithm has been developed and applied for high-complexity VLSI designs.<>