Computing Exact Minimum Cuts Without Knowing the Graph

@article{Rubinstein2018ComputingEM,
  title={Computing Exact Minimum Cuts Without Knowing the Graph},
  author={A. Rubinstein and T. Schramm and S. M. Weinberg},
  journal={ArXiv},
  year={2018},
  volume={abs/1711.03165}
}
  • A. Rubinstein, T. Schramm, S. M. Weinberg
  • Published 2018
  • Computer Science, Mathematics
  • ArXiv
  • 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… CONTINUE READING
    Quantum algorithms for graph problems with cut queries
    Weighted min-cut: sequential, cut-query, and streaming algorithms
    9
    Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms
    1
    Polynomial pass lower bounds for graph streaming algorithms
    9
    Graph Connectivity and Single Element Recovery via Linear and OR Queries

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 31 REFERENCES
    Fast Augmenting Paths by Random Sampling from Residual Graphs
    6
    Near-Linear Query Complexity for Graph Inference
    7
    Optimally reconstructing weighted graphs using queries
    23
    A new approach to the minimum cut problem
    399
    Reconstructing Weighted Graphs with Minimal Query Complexity
    12
    Optimal query complexity bounds for finding graphs
    20
    Graph Reconstruction via Distance Oracles
    11