Faster Algorithms for Next Breakpoint and Max Value for Parametric Global Minimum Cuts

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 \(\mu \in \mathbb {R}^d\) 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.

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