A Note on Maximum Integer Flows in Directed Planar Graphs with Vertex Capacities

01/27/2021

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by   Dor Mesica, et al.

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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 polylog(nU)) where k is the number of sources and sinks, and U is the largest capacity of a single vertex. In this work we give a faster implementation for a procedure used by Wang's algorithm, improving the overall running time of his algorithm to O(k^4n polylog(nU))