Before revision: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019 runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
After revision: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019 runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog(nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks. This improves by a factor of k^2 over the fastest algorithm previously known for this problem ]