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Computing Exact Minimum Cuts Without Knowing the Graph

Authors Aviad Rubinstein, Tselil Schramm, S. Matthew Weinberg

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Aviad Rubinstein
Tselil Schramm
S. Matthew Weinberg

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Aviad Rubinstein, Tselil Schramm, and S. Matthew Weinberg. Computing Exact Minimum Cuts Without Knowing the Graph. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 39:1-39:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ITCS.2018.39

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 \ 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).
Keywords
  • query complexity
  • minimum cut

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