Reactive Proximity Data Structures for Graphs

@article{Eppstein2018ReactivePD,
  title={Reactive Proximity Data Structures for Graphs},
  author={David Eppstein and Michael T. Goodrich and Nil Mamano},
  journal={ArXiv},
  year={2018},
  volume={abs/1803.04555}
}
We consider data structures for graphs where we maintain a subset of the nodes called sites, and allow proximity queries, such as asking for the closest site to a query node, and update operations that enable or disable nodes as sites. We refer to a data structure that can efficiently react to such updates as reactive. We present novel reactive proximity data structures for graphs of polynomial expansion, i.e., the class of graphs with small separators, such as planar graphs and road networks… 
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