Planar Distance Oracles with Better Time-Space Tradeoffs

@inproceedings{Long2021PlanarDO,
  title={Planar Distance Oracles with Better Time-Space Tradeoffs},
  author={Yaowei Long and Seth Pettie},
  booktitle={SODA},
  year={2021}
}
In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann (STOC 2019) showed that exact distance queries on planar graphs could be answered in $n^{o(1)}$ time by a data structure occupying $n^{1+o(1)}$ space, i.e., up to $o(1)$ terms, optimal exponents in time (0) and space (1) can be achieved simultaneously. Their distance query algorithm is recursive: it makes successive calls to a point-location algorithm for planar Voronoi diagrams, which involves many recursive distance… 
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