Before revision:  These circulations are derived by computing a regularized version of the standard Newton step, which can be done efficiently due to recent developments on computing \ell_p-norm minimizing flows (Kyng-Peng-Sachdeva-Wang  ).
After revision:  These circulations are derived by computing a regularized version of the standard Newton step, which is partially inspired by previous work on the unit-capacity maximum flow problem (Liu-Sidford, 2019), and subsequently refined based on the very recent progress on this problem (Liu-Sidford, 2020). The resulting step problem can then be computed efficiently using the recent work on \ell_p-norm minimizing flows (Kyng-Peng-Sachdeva-Wang ).