  Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut
in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that
the approximation ratio of the Goemans-Williamson algorithm is optimal assuming
Khot's Unique Games Conjecture [SICOMP'07]. In the problem of maximum cuts in
directed graphs (Max-DiCut), in which we seek as many edges going from one
particular side of the cut to the other, the situation is more complicated but
the recent work of Brakensiek, Huang, Potechin, and Zwick showed that their
0.874-approximation algorithm is tight under the Unique Games Conjecture (up to
a small delta)[FOCS'23].
  We consider a promise version of the problem and design an SDP-based
algorithm which, if given a directed graph G that has a directed cut of value
rho, finds an undirected cut in G (ignoring edge directions) with value at
least \rho.
