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 ⊂ V , the oracle returns the size of the cut between S and V \ S. We provide algorithms computing an exact minimum s-t cut in G with O(n 5/3 ) queries, and computing an exact global minimum cut of G with only O(n) queries (while learning the graph requires Θ(n 2 ) queries).
Similarly, in REF , for designing algorithms with better query complexity for the Min-Cut and s − tMin-Cut problems, for a graph G, the oracle took as input a vertex subset S ⊆ V (G) and output the value c(S) of the cut between S and V (G) \ S. The corresponding query complexities for the Min-Cut and s − t-Min-Cut problems are O(n) and O(n 5/3 ) 2 ; respectively.
Computing exact minimum cuts without knowing the graph
ArXiv
ArXiv
Mathematics Computer Science