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 \ 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 ~{\Theta}(n^2) queries).
@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2018.39, author = {Rubinstein, Aviad and Schramm, Tselil and Weinberg, S. Matthew}, title = {{Computing Exact Minimum Cuts Without Knowing the Graph}}, booktitle = {9th Innovations in Theoretical Computer Science Conference (ITCS 2018)}, pages = {39:1--39:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-060-6}, ISSN = {1868-8969}, year = {2018}, volume = {94}, editor = {Karlin, Anna R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.39}, URN = {urn:nbn:de:0030-drops-83168}, doi = {10.4230/LIPIcs.ITCS.2018.39}, annote = {Keywords: query complexity, minimum cut} }
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