Multiple-Source Single-Sink Maximum Flow in Directed Planar Graphs in   O(diameter*n*log(n)) Time
  We develop a new technique for computing maximum flow in directed planar graphs with multiple sources and a single sink that significantly deviates from previously known techniques for flow problems. This gives rise to an O(diameter*n*log(n)) algorithm for the problem. 
Philip N. Klein and Shay Mozes
cs.DM cs.DS