Direct, problem-specific analysis of SuperGreedy++ for minimum s–t cut

Develop a direct, problem-specific theoretical analysis for SuperGreedy++ when applied to the minimum s–t cut problem formulated as Submodular Function Minimization, establishing convergence guarantees or approximation bounds without relying on reductions through the Minimum Norm Point problem.

Background

The authors show that SuperGreedy++—originally designed for Densest Supermodular Set—can be interpreted as an algorithm for Submodular Function Minimization and performs strongly on minimum s–t cut instances in practice.

Their current guarantees are derived via reductions to the Minimum Norm Point problem, and they highlight the need for a direct, problem-specific analysis for settings like minimum s–t cut.