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Are there any non-trivial bounds on the space complexity of global minimum cut? The problem is known to be in $\mathsf{RNC}$. Is anything known about containment in either $\mathsf{L}$ or $\mathsf{NL}$?

Such a bound seems unlikely for the space-complexity of s-t minimum cut given that maximum flow is $\mathsf{P}$-complete.

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    $\begingroup$ Is global mincut in NC? I think it is only known to be in RNC. Look in Karger's paper dl.acm.org/citation.cfm?id=331608. $\endgroup$ – Chandra Chekuri Sep 2 at 16:56
  • $\begingroup$ Sorry, you are absolutely correct (updated to RNC in the original post). I don't know of any NC algorithms for global min cut. The fastest deterministic sequential algorithm seems to be due to Kawarabayashi and Thorup (dl.acm.org/citation.cfm?id=2746588). $\endgroup$ – xal Sep 2 at 20:44

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