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arXiv · 1711.03165

Computing exact minimum cuts without knowing the graph

Aviad Rubinstein·Tselil Schramm·S. Matthew Weinberg
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Abstract

We give query-efficient algorithms for the global min-cut and the s-t cut problem in unweighted, undirected graphs. Our oracle model is inspired by the submodular function minimization problem: on query $S \subset V$, the oracle returns the size of the cut between $S$ and $V \setminus S$. We provide algorithms computing an exact minimum $s$-$t$ cut in $G$ with $\tilde{O}(n^{5/3})$ queries, and computing an exact global minimum cut of $G$ with only $\tilde{O}(n)$ queries (while learning the graph requires $\tilde{\Theta}(n^2)$ queries).

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Aviad Rubinstein, Tselil Schramm, S. Matthew Weinberg. 2017-11-08. Computing exact minimum cuts without knowing the graph. https://arxiv.org/abs/1711.03165

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