Planar Graphs, Negative Weight Edges, Shortest Paths, Near Linear Time
نویسندگان
چکیده
In this paper, we present an O(n log3 n) time algorithm for finding shortest paths in a planar graph with real weights. This can be compared to the best previous strongly polynomial time algorithm developed by Lipton, Rose, and Tarjan in 1978 which ran in O(n3=2) time, and the best polynomial algorithm developed by Henzinger, Klein, Subramanian, and Rao in 1994 which ran in e O(n4=3) time. We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.
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