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SODA
2010
ACM

Maximum Flows and Parametric Shortest Paths in Planar Graphs

14 years 1 months ago
Maximum Flows and Parametric Shortest Paths in Planar Graphs
We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G . This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(nlog n) time. As we continuously increase the parameter, each change in the shortest path tree can be effected in O(log n) time using standard dynamic tree data structures, and the special structure of the parametrization implies that each directed edge enters the evolving shortest path tree at most once. The resulting maximum-flow algorithm is identical to the recent algorithm of Borradaile and Klein [J. ACM 2009], but our new formulation allows a simpler presentation and analysis. On the other hand, we demonstrate that for a similarly structured parametric shortest path problem on the torus, the shortest path tree can change (n2 ) times in the worst case, suggesting that a different method may be required to efficiently c...
Jeff Erickson
Added 01 Mar 2010
Updated 02 Mar 2010
Type Conference
Year 2010
Where SODA
Authors Jeff Erickson
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