Single Source -- All Sinks Max Flows in Planar Digraphs

@article{Lacki2012SingleS,
  title={Single Source -- All Sinks Max Flows in Planar Digraphs},
  author={Jakub Lacki and Yahav Nussbaum and Piotr Sankowski and Christian Wulff-Nilsen},
  journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science},
  year={2012},
  pages={599-608}
}
Let G = (V, E) be a planar n-vertex digraph. Consider the problem of computing max st-flow values in G from a fixed source s to all sinks t ϵ V \ {s}. We show how to solve this problem in near-linear O(n log3 n) time. Previously, nothing better was known than running a single-source singlesink max How algorithm n-1 times, giving a total time bound of O(n2 log n) with the algorithm of Borradaile and Klein. An important implication is that all-pairs max st-How values in G can be computed in near… CONTINUE READING
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