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The Karger-Stein Algorithm is Optimal for k-cut
[article]

2019
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arXiv
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pre-print

In the k-cut problem, we are given an edge-weighted graph and want to find the least-weight set of edges whose deletion breaks the graph into k connected components. Algorithms due to Karger-Stein and Thorup showed how to find such a minimum k-cut in time approximately O(n^2k-2). The best lower bounds come from conjectures about the solvability of the k-clique problem and a reduction from k-clique to k-cut, and show that solving k-cut is likely to require time Ω(n^k). Our recent results have

arXiv:1911.09165v1
fatcat:5mepusz5pbe63nzeyxlngwtf4m