Computing exact minimum cuts without knowing the graph

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 $\tilde{O}(n<sup>{5/3})$ queries, and computing an exact global minimum cut of $G$ with only $\tilde{O}(n)$ queries (while learning the graph requires $\tilde{\Theta}(n<sup>2)$ queries).