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We consider the minimum s, t-cut problem in a network with parametrized arc capacities. Following the seminal work of Gallo et al. (SIAM J. Comput. 18(1):30–55, 1989), classes of this parametric problem have been shown to enjoy the nice Structural Property that minimum cuts are nested, and the nice Algorithmic Property that all minimum cuts can be computed in the same asymptotic time as a single minimum...
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