 Our result immediately implies a strongly polynomial algorithm for the Submodular Function Minimization problem that makes at most O(n^3) calls to an evaluation oracle . This improves upon the previously best O(n^3 \log^2(n)) oracle complexity for strongly polynomial algorithms given in [Lee, Sidford and Wong, FOCS 2015] and [Dadush, V\'egh and Zambelli, SODA 2018], and an exponential time algorithm with oracle complexity O(n^3 \log(n)) given in the former work.
<fluency>  Our result immediately implies a strongly polynomial algorithm for the Submodular Function Minimization problem that makes at most O(n^3) calls to an evaluation oracle . This improves upon the previously best O(n^3 \log^2(n)) oracle complexity for strongly polynomial algorithms given in [Lee, Sidford and Wong, FOCS 2015] and [Dadush, V\'egh and Zambelli, SODA 2018], and an exponential time algorithm with oracle complexity O(n^3 \log(n)) given in the former work.
 Our result immediately implies a strongly polynomial algorithm for the Submodular Function Minimization problem that makes at most O(n^3) calls to an evaluation oracle , and an exponential time algorithm that makes at most O(n^2 \log(n)) calls to an evaluation oracle. These improve upon the previously best O(n^3 \log^2(n)) oracle complexity for strongly polynomial algorithms given in [Lee, Sidford and Wong, FOCS 2015] and [Dadush, V\'egh and Zambelli, SODA 2018], and an exponential time algorithm with oracle complexity O(n^3 \log(n)) given in the former work.