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

Abolfazl Hassanpour (), Massoud Aman () and Alireza Ebrahimi ()
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Abolfazl Hassanpour: University of Birjand
Massoud Aman: University of Birjand
Alireza Ebrahimi: Yazd University

Journal of Combinatorial Optimization, 2024, vol. 48, issue 5, No 1, 22 pages

Abstract: Abstract Planar hypergraphs are widely used in several applications, including VLSI design, metro maps, information visualisation, and databases. The minimum $$ s-t $$ s - t hypercut problem in a weighted hypergraph is to find a partition of the vertices into two nonempty sets, S and $$ \overline{S} $$ S ¯ , with $$s\in S$$ s ∈ S and $$t\in \overline{S}$$ t ∈ 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 $$ s-t $$ 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.

Keywords: Planar hypergraph; Minimum $$ s-t $$ s - t hypercut; Maximum $$ s-t $$ s - t flow; Shortest path; Polynomial time algorithm; VLSI circuits (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01231-w

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