Planar Reachability Under Single Vertex or Edge Failures

@inproceedings{Italiano2021PlanarRU,
  title={Planar Reachability Under Single Vertex or Edge Failures},
  author={Giuseppe F. Italiano and Adam Karczmarz and Nikos Parotsidis},
  booktitle={SODA},
  year={2021}
}
In this paper we present an efficient reachability oracle under single-edge or single-vertex failures for planar directed graphs. Specifically, we show that a planar digraph G can be preprocessed in O(n log n/log logn) time, producing an O(n log n)-space data structure that can answer in O(log n) time whether u can reach v in G if the vertex x (the edge f) is removed from G, for any query vertices u, v and failed vertex x (failed edge f). To the best of our knowledge, this is the first data… Expand

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