Optimal Bounds for the k-cut Problem

@article{Gupta2022OptimalBF,
  title={Optimal Bounds for the k-cut Problem},
  author={Anupam Gupta and David G. Harris and Euiwoong Lee and Jason Li},
  journal={ACM Journal of the ACM (JACM)},
  year={2022},
  volume={69},
  pages={1 - 18}
}
In the k-cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into k connected components. Algorithms of Karger and Stein can solve this in roughly O(n2k) time. However, lower bounds from conjectures about the k-clique problem imply that Ω (n(1-o(1))k) time is likely needed. Recent results of Gupta, Lee, and Li have given new algorithms for general k-cut in n1.98k + O(1) time, as well as specialized algorithms with better performance for certain… 

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