Oracles for bounded-length shortest paths in planar graphs

@article{Kowalik2006OraclesFB,
  title={Oracles for bounded-length shortest paths in planar graphs},
  author={Lukasz Kowalik and Maciej Kurowski},
  journal={ACM Trans. Algorithms},
  year={2006},
  volume={2},
  pages={335-363}
}
We present a new approach for answering short path queries in planar graphs. For any fixed constant k and a given unweighted planar graph G = (V, E), one can build in O(|V|) time a data structure, which allows to check in O(1) time whether two given vertices are at distance at most k in G and if so a shortest path between them is returned. Graph G can be undirected as well as directed.Our data structure works in fully dynamic environment. It can be updated in O(1) time after removing an edge or… Expand
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