Effect of Constant One and Zero, Shared and Non-decomposed Nodes on Runtime and Graph Size of the Shannon Factor Graph (SFG)

In this paper, we propose two different algorithms for Shannon Factor Graph (SFG) construction, which can be used for cut-less mapping, to improve the runtime, graph size and required memory size. The first SFG construction algorithm does not consider the nature of the nodes (constant one and zero, non-decomposed and shared nodes) while building the SFG, whereas the second algorithm finds out the nature of the nodes on-the-fly. We observed that the constant one and zero, Shared and non-decomposed nodes can be used at the time of SFG construction to minimize the runtime and graph size significantly and to make the graph semi-canonical. The theoretical analysis and experiments performed on the standard benchmark circuits show that, by finding the constant one and zero, shared and non-decomposed nodes on-the-fly reduces the graph size by a factor of 126 and the runtime by a factor of 5.5.