Optimal min-area min-cut replication in partitioned circuits

Previous results show that node replication can be used to reduce the number of cut edges substantially in a partitioned circuit. The node replication approach is particularly useful for fully utilizing pin-limited devices such as multiple field-programmable gate array. Hwang and El Gamal [1992, 1995] formulated the min-cut replication problem, which is to determine min-cut replication sets for the components of a k-way partition such that the cut size of the partition is minimized after the replication. They gave an optimal algorithm for finding min-cut replication sets for a k-way partitioned digraph. However their optimal min-cut replication algorithm does not guarantee min-cut replication sets of minimum sizes. Furthermore, their algorithm is not optimal for hypergraphs. In this paper, we optimally solve the min-area min-cut replication problem on digraphs, which is to find min-cut replication sets with the minimum sizes. More important, we give an optimal solution to the hypergraph min-area min-cut replication problem using a much smaller flow network model. We implemented our algorithms in a package called Hyper-MAMC, and interfaced Hyper-MAMC to the TAPIR package. We compared the replication results by Hyper-MAMC with those obtained by MC-Rep in the TAPIR package on the exact same initial partitions of a set of MCNC Partition93 benchmark circuits. On average, Hyper-MAMC produces 57.3% fewer cut nets and runs much faster than MC-Rep