Shortest Paths in Planar Graphs with Real Lengths in $O(n\log^2n/\log\log n)$ Time

Details Shortest Paths in Planar Graphs with Real Lengths in $O(n\log^2n/\log\log n)$ Time Shortest Paths in Planar Graphs with Real Lengths in $O(n\log^2n/\log\log n)$ Time

2009-11-25

arxiv.org/abs/0911.4963v1

Computer Science

Discrete Mathematics

Scientific paper

Given an $n$-vertex planar directed graph with real edge lengths and with no
negative cycles, we show how to compute single-source shortest path distances
in the graph in $O(n\log^2n/\log\log n)$ time with O(n) space. This is an
improvement of a recent time bound of $O(n\log^2n)$ by Klein et al.

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