Enumerating the min-cuts for applications to graph extraction under size constraints

Given an undirected hypergraph G₀ with two vertices s and t specified, our problem is to extract a maximal subgraph under a constraint. It comprises two terms, the upper bound of the area and the cut separating the subgraph being an s-t minimum cut. If G₀ is a model of a logic circuit, this is a faithful problem formulation in implementation of PPGA or MCM. Aiming to support such a design, we propose a representation of the s-t minimum cut of G₀ in terms of a directed acyclic graph G*. The key idea is to transform G₀ to a directed flow-graph with source s and sink t by a known technique and, after finding a maximum flow, to traverse the graph by a forward-search, which we introduce here