# Compact oracles for reachability and approximate distances in planar digraphs

@article{Thorup2001CompactOF, title={Compact oracles for reachability and approximate distances in planar digraphs}, author={Mikkel Thorup}, journal={Proceedings 2001 IEEE International Conference on Cluster Computing}, year={2001}, pages={242-251} }

It is shown that a planar digraph can be preprocessed in near-linear time, producing a near-linear space distance oracle that can answer reachability queries in constant time. The oracle can be distributed as an O(log n) space label for each vertex and then we can determine if one vertex can reach another considering their two labels only. The approach generalizes to approximate distances in weighted planar digraphs where we can then get a (1+/spl epsi/) approximation distance in O(log log /spl…

## 215 Citations

### More Compact Oracles for Approximate Distances in Planar Graphs

- Computer ScienceArXiv
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This paper gives the first improvements on the space-querytime tradeoff for planar graphs, improving upon Thorup's oracle both in terms of eps and n and believes that the dependency on eps may be almost optimal.

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### Fast and Compact Exact Distance Oracle for Planar Graphs

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An O(n 5/3)-space distance oracle which answers exact distance queries in O(log n) time for n-vertex planar edge-weighted digraphs is introduced.

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To the best of the knowledge, this is the first fully dynamic strong-connectivity algorithm achieving both sublinear update time and polylogarithmic query time for an important class of digraphs.

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