Before revision: We show the existence of an exact mimicking network of k^{O(\log k)} edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals . Furthermore, if Small Set Expansion has an approximation algorithm with a ratio slightly better than \Theta(\log n), then a mimicking network of quasipolynomial size can be computed in polynomial time.
After revision: We show the existence of an exact mimicking network of k^{O(\log k)} edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals , as well as a method for computing a mimicking network of quasipolynomial size can be computed in polynomial time.