  In this note, we present a simple differentially private algorithm for the
global minimum cut problem using only one call to the exponential mechanism.
This problem was first studied by Gupta et al. [2010], and they gave a
differentially private algorithm with near-optimal utility guarantees. We
improve upon their work in many aspects: our algorithm is simpler, more
natural, and more efficient than the one given in Gupta et al. [2010], and
furthermore provides slightly better privacy and utility guarantees.
