The parametric global minimum cut problem concerns a graph G=(V,E) where the cost of each edge is an affine function of a parameter μ∈Rd for some fixed dimension d. We consider the problems of finding the next breakpoint in a given direction, and finding a parameter value with maximum minimum cut value. We develop strongly polynomial algorithms for these problems that are faster than a naive application of Megiddo's parametric search technique. Our results indicate that the next breakpoint problem is easier than the max value problem.
@article{arxiv.1911.11847,
title = {Faster Algorithms for Parametric Global Minimum Cut Problems},
author = {Hassene Aissi and S. Thomas McCormick and Maurice Queyranne},
journal= {arXiv preprint arXiv:1911.11847},
year = {2019}
}