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 $\tilde{O}(n^{5/3})$ queries, and computing an exact global minimum cut of $G$ with only $\tilde{O}(n)$ queries (while learning the graph requires $\tilde{\Theta}(n^2)$ queries).
- Publication:
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arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.03165
- arXiv:
- arXiv:1711.03165
- Bibcode:
- 2017arXiv171103165R
- Keywords:
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- Computer Science - Data Structures and Algorithms