The optimal circuit decompositions using network flow formulations

Several decomposition criteria to decompose circuits are presented; i.e. the flux cut A, the flux cut B, the cost ratio cut and one generalized minimum cut. The flux cut B is an extension of the flux cut A. The cost ratio cut generates the optimal partitioning for a linear placement problem. The generalized minimum cut uses a cost function related to a polynomial function of the sizes of two partitioned subsets. The physical meaning of the cuts is described. The decomposition problems are shown to be strongly related to the communication problems. Several network flow models are constructed. Relations between the maximum flow solutions and the minimum partitionings are illustrated. Linear programming is used to formulate the proposed maximum flow problems. The duality techniques of linear programming are utilized to derive the relation to the optimal partition solution