Minimum $$ s-t $$ hypercut in (s, t)-planar hypergraphs

Planar hypergraphs are widely used in several applications, including VLSI design, metro maps, information visualisation, and databases. The minimum \( s-t \) hypercut problem in a weighted hypergraph is to find a partition of the vertices into two nonempty sets, S and \( \overline{S} \), with \(s\in S\) and \(t\in \overline{S}\) that minimizes the total weight of hyperedges that have at least two endpoints in two different sets. In the present study, we propose an approach that effectively solves the minimum \( s-t \) hypercut problem in (s, t)-planar hypergraphs. The method proposed demonstrates polynomial time complexity, providing a significant advancement in solving this problem. The modelling example shows that the proposed strategy is effective at obtaining balanced bipartitions in VLSI circuits.